Preliminary design of a micro launch vehicle

Ana Rita Afonso Rebelo

Thesis to obtain the Master of Science Degree in Aerospace Engineering

Supervisors: Prof. António Manuel Relógio Ribeiro Prof. Filipe Szolnoky Ramos Pinto Cunha

Examination Committee Chairperson: Prof. Fernando José Parracho Lau Supervisor: Prof. Filipe Szolnoky Ramos Pinto Cunha Member of the Committee: Prof. André Calado Marta

June 2018 ii Acknowledgments

First of all, I would like to thank Omnidea for the wonderful opportunity to be a part of this incredible project. A special acknowledgement must be extended to Engineer Horacio´ Moreira, for his guidance and seemingly inexhaustible availability through the duration of this work. I would also like to thank Professor Relogio´ Ribeiro and Professor Filipe Cunha for their vital advices and sharp insights. Particular gratitude must be offered to my parents, for always encouraging me to pursue my dreams and giving me unconditional support. To Miguel, without whom the last years would not be anywhere near as fun. Thank you for always being there for me. Finally, I would also like to thank Ana and Pedro, who took the black with me and without whom I would not have made it this far, and to Lu´ıs for being a patient “Thesaurus”. Thank you to everyone who was a part of this journey.

iii iv Resumo

O dimensionamento estrutural preliminar de um lanc¸ador e´ um dos passos fundamentais na concepc¸ao˜ do ve´ıculo em geral. Dos varios´ subsistemas que o compoe,˜ a par do propulsivo, e´ a estrutura o mais condicionante, pois define a maior percentagem de massa seca do ve´ıculo. Consequentemente, um dos objectivos principais num projecto de um lanc¸ador e´ diminuir a sua massa estrutural, de forma a maxi- mizar a razao˜ entre a carga a colocar em orbita´ e o peso total do ve´ıculo, maximizando deste modo a eficienciaˆ de cada missao.˜ Assim, a analise´ estrutural preliminar e´ essencial na optimizac¸ao˜ do projecto e e´ a finalidade deste trabalho. Comec¸a-se por uma revisao˜ bibliografica,´ nao˜ so´ sobre os componentes estruturais que constituem um lanc¸ador e os respectivos materiais, mas tambem´ sobre os combust´ıveis que podem ser selecionados neste caso. De seguida, atraves´ de trade-off studies, sao˜ entao˜ definidos esses combust´ıveis e materiais estruturais: oxigenio´ l´ıquido e metano l´ıquido como combust´ıveis; a liga de alum´ınio 2024 e um composito´ de fibra de carbono de alta resistenciaˆ como materiais. Posto isto, primeiramente e´ feito o dimensionamento estrutural, com o intuito de avaliar quais as dimensoes˜ gerais (comprimento e diametro)ˆ que proporcionam as melhores caracter´ısticas aerodinamicasˆ ao lanc¸ador. Por fim, estando estabelecido o coeficiente de esbeltez do ve´ıculo, e´ poss´ıvel determinar os parametrosˆ dimensionais de cada componente estrutural, utilizando a Teoria da Membrana aplicada a cascas de revoluc¸ao.˜ Conclui-se que o ve´ıculo tera´ menor massa do que inicialmente estimado, o que significa que existe uma margem para futuras iterac¸oes˜ na sua concepc¸ao.˜

Palavras-chave: Lanc¸ador, tanques estruturais, dimensionamento estrutural, cascas de revoluc¸ao,˜ teoria da membrana

v vi Abstract

The preliminary structural sizing of a launcher is one of the fundamental steps in the design of that vehicle. From the various subsystems that it comprises, along with the propulsion, it is the structure the most conditioning one, since it defines the major percentage of the vehicle’s dry mass. Consequently, one of the main goals in a launch vehicle project is to decrease its structural mass, in order to maximize the ratio between the payload and the launcher’s total weight, thus also maximizing the efficiency of each mission. Therefore, a preliminary structural analysis is essential in the design optimization and it is the goal of this work. To begin with, a bibliographic revision is done, not only about the structural components that form the launcher and their respective materials, but also about the propellants that can be selected in this case. Next, those propellants and structural materials are defined through trade- off studies: liquid oxygen and liquid methane as propellants; the aluminium alloy 2024 and the High Strength Carbon Fiber Composite as the materials. After that, the sizing is first done with the aim of evaluating which are the general dimensions (length and diameter) that provide the best aerodynamic characteristics to the launcher. Finally, having established the fineness ratio of the vehicle, it is possible to determine the dimensional parameters of each structural element, utilizing the Membrane Theory for shells of revolution. It is concluded that the vehicle has a lower mass than initially estimated, meaning that there is a margin for future design iterations.

Keywords: Launcher, structural tanks, structural sizing, shells of revolution, Membrane Theory

vii viii Contents

Acknowledgments...... iii Resumo...... v Abstract...... vii List of Tables...... xi List of Figures...... xiii Nomenclature...... xv Glossary...... xxi

1 Introduction 1 1.1 Motivation...... 1 1.2 Topic Overview and Requirements...... 2 1.3 Thesis Outline...... 3

2 Bibliographic Revision5 2.1 Structural Components...... 5 2.1.1 Tanks...... 6 2.1.2 Adapters...... 8 2.1.3 Payload Fairing and Nose Cones...... 9 2.1.4 Thrust Frame...... 9 2.1.5 Secondary Structures...... 10 2.2 Propulsion...... 10 2.2.1 Type of Propulsion...... 11 2.2.2 Feeding System...... 13 2.3 Materials in Launch Vehicles...... 14

3 Trade-off Studies 19 3.1 Comparison of Propellants...... 19 3.1.1 Propellants Selection Criteria...... 20 3.1.2 Propellant Selection...... 24 3.2 Comparison of Materials...... 24 3.2.1 Materials Selection Criteria...... 25 3.2.2 Material Selection...... 27

ix 4 External Preliminary Sizing 31 4.1 Atmospheric Model...... 31 4.1.1 Temperature...... 31 4.1.2 Pressure...... 32 4.1.3 Density...... 33 4.1.4 Mach number...... 34 4.2 Rigid Body Forces...... 35 4.2.1 Thrust...... 35 4.2.2 Drag Force...... 36 4.2.3 Gravity Force...... 45 4.3 Launcher Preliminary Sizing...... 46

5 Structural sizing 53 5.1 Tanks’ Architecture...... 53 5.2 Structural Loading...... 57 5.2.1 Lift-off...... 58 5.2.2 Maximum Drag...... 58 5.3 Analytical Method...... 59 5.3.1 Shells of Revolution...... 61 5.3.2 Cylindrical Shells...... 64 5.3.3 Materials’ Properties...... 66 5.3.4 Analytical Results...... 66 5.4 Numerical Results...... 67

6 Conclusion 69 6.1 Achievements...... 69 6.2 Future Work...... 70

Bibliography 71

A Propellants Reliability 81 A.1 Launch Vehicles Failures...... 81

B Structural Mass of Various Tank Geometries 85

C Analytical Sizing 89 C.1 Second Stage...... 89 C.2 First Stage...... 91

D Launch Vehicle Layout 93

x List of Tables

1.1 Operational requirements...... 3

3.1 Selected propellant combinations characteristics...... 19 3.2 Tanks mass estimation results...... 21 3.3 Propellants cost...... 22 3.4 Reliability of each propellant combination...... 24 3.5 Propellants selection matrix...... 24 3.6 Properties of some commonly used materials...... 25 3.7 Comparison of various aluminium and steel alloys properties at room temperature.... 28 3.8 Decision matrix for the tanks material...... 28 3.9 Comparison of various aluminium alloys and High-Strength composites properties at room temperature...... 29 3.10 Decision matrix for the adapters material...... 29 3.11 Decision matrix for the payload fairing material...... 29 3.12 Selected material for each structural component...... 30

4.1 Variation of Tb, Lb and Zb for each layer...... 32

4.2 Variation of Pb for each layer...... 33 4.3 Air pressure variation for altitudes above 86 km...... 33

4.4 Variation of ρb for each layer...... 34 4.5 Air density variation for altitudes above 86 km...... 34 4.6 Results of the comparison between the two base drag models for supersonic velocities. 42 4.7 Expressions to be used to determine the drag force coefficients...... 45 4.8 Total volume of propellant tanks...... 47 4.9 Small satellites characteristics...... 47 4.10 Propellant and structural mass of the second stage for each fineness ratio...... 50 4.11 Dimensions of the launch vehicle...... 51

5.1 Total volume of propellants...... 54 5.2 Structural mass of each configuration type...... 55 5.3 Trade-off study results for the second stage tanks configuration...... 56 5.4 Safety, project and model factors typical values...... 60

xi 5.5 Properties of the selected materials...... 66 5.6 Analytical results...... 67 5.7 Comparison of the analytical and numerical results for each structural component.... 68

A.1 Active launch vehicles that suffered failures in the past 10 years [82]...... 81 A.2 Number of stages launched and number of failures related to each propellant combination 84

xii List of Figures

1.1 Velocity and mass variation with time...... 3

2.1 Example of a launch vehicle’s structural components. Adapted from [4]...... 5 2.2 Example of spherical tanks: N1 Rocket. Reproduced from [8]...... 7 2.3 Possible tank geometric shapes. Adapted from [7]...... 7 2.4 Possible tank architectures. Reproduced from [1]...... 8 2.5 Adapter examples...... 8 2.6 Fairing examples...... 9 2.7 Thrust frame examples...... 10 2.8 Schematics of a liquid rocket engine. Reproduced [16]...... 11

2.9 Comparison between theoretical Isp of various propellants. Reproduced from [17]..... 12 2.10 Propulsion feed systems. Adapted from [18]...... 13

4.1 Speed of sound and Mach number variation with altitude...... 35 4.2 Net force applied on the launch vehicle...... 35 4.3 Thrust and vertical acceleration variation with time...... 36 4.4 Launch vehicle scheme. Adapted from [55]...... 37 4.5 Comparison between the two models for the turbulent friction coefficient...... 39 4.6 Comparison between the two models for the compressible friction coefficients...... 39 4.7 Base drag coefficient variation with Mach number. Adapted from [59]...... 40 4.8 Comparison between the two base drag models for subsonic velocities...... 41 4.9 Comparison between the two base drag models for Mach numbers between 0.3 and 1.. 41 4.10 Base drag variation of a body of revolution according to Barrowman. Adapted from [52].. 42 4.11 Forepressure drag for transonic speeds. Adapted from [50]...... 43 4.12 Forepressure drag for supersonic speeds. Adapted from [50]...... 44 4.13 Payload configuration...... 47 4.14 Illustration of the geometrical similarity of triangles...... 48 4.15 Iterative process to determine the volume requirements of the vehicle...... 51 4.16 Scheme of a tangent ogive. Adapted from [60]...... 52 4.17 Launch vehicle overall dimensions diagram (in meters)...... 52

5.1 Possible tank geometric configurations...... 54

xiii 5.2 Packaging of each tank configuration...... 55 5.3 Second stage tanks configuration and main dimensions (in meters)...... 57 5.4 First stage tanks configuration and main dimensions (in meters)...... 57 5.5 Net force variation with altitude...... 58 5.6 Pressure and velocity variation at M=1.2...... 59 5.7 Development approach for each structural element. Reproduced from [77]...... 60 5.8 Ilustration of a shell element. Reproduced from [79]...... 61 5.9 Ogival shell. Adapted from [79]...... 62 5.10 Illustration of a cylindrical shell element. Reproduced from [79]...... 64

B.1 Separate tanks configuration...... 85 B.2 Common bulkhead tanks configuration...... 86 B.3 Toroidal tanks configuration...... 87

C.1 Structural components of the second stage...... 89 C.2 Structural components of the first stage...... 91

xiv Nomenclature

Greek symbols

∆γ Increase in the buckling correlation factor due to internal pressure.

∆v Velocity gain.

∆vD Drag losses - decrease in the velocity due to the drag force.

∆veff Theoretical velocity that the vehicle needs to reach orbit without considering gravity or drag losses.

∆vthrust Total velocity that the vehicle needs to reach orbit.

∆vw Gravity losses - decrease in the velocity due to gravity.

δ Applied force per unit volume of the shell.

γ Ratio of specific heats; Propellant specific weight; Correlation factor for the classical critical buckling stress.

λ Geometry parameter to determine spherical cap buckling pressure.

µ Dynamic viscosity of air.

ν Poisson’s ratio of a material.

φ Meridional angle.

φ0 Angle between the meridian and the axis of the ogive.

ρ Air density.

ρb Reference air density of layer b.

ρm Material density.

σφ Meridional stress.

σa Axial stress.

σCL Classical buckling stress.

xv SP 8007 σcr Critical buckling stress according to NASA SP-8007.

σu Tensile/ultimate strength.

σy Yield stress.

σθ Circumferential/hoop stress.

σcra/b Combined critical stress in case of axial and bending loads and internal pressure.

σcra Combined critical stress in case of axial loads and internal pressure.

σcrb Combined critical stress in case of bending loads and internal pressure.

θc Semivertex angle of a cone.

ϕ Flight path angle.

Roman symbols

A Projected area. a Speed of Sound; Acceleration. a, b, c Payload dimensions; Ellipsoidal semi-axis.

CD Drag coefficient.

D Drag force.

Db Base drag.

Df Friction drag.

Dw Nose-wave drag. d Diameter.

E Modulus of elasticity of a material.

G Gravitational constant. g Gravitational acceleration. gl Lateral acceleration. hCG Height of a component’s gravity center.

I Second moment of area.

Isp Specific Impulse.

L Length.

L1 Length of the cylindrical part of the first stage.

xvi L2 Length of the cylindrical part of the second stage.

Lb Temperature gradient of layer number b.

Lcyl Length of the cylindrical part of a toroidal tank.

Lfuel Length of the fuel tank cylindrical part.

Lox Length of the oxidizer tank cylindrical part.

Ln Length of the payload fairing.

Lt Total vehicle’s length.

M Mach number; Mean molecular mass of air.

M⊕ Earth’s mass.

Mbody Margin applied to the launch vehicle’s mass, without the payload.

Mb Bending moment.

Me Engines’ mass.

Mnose Margin applied to the payload fairing’s and adapters’ mass.

MP Payload’s mass. m Mass. mbody Launch vehicle’s mass without the payload fairing, at given point. mf Stage mass at burn-out. mi Stage mass at lift-off. mnose Payload fairing plus payload mass. mpropellant Total propellant mass. mstr Structural mass. mtotal Launch vehicle’s total mass at given point. mupp Mass that a stage supports.

P Atmospheric pressure.

Pa Axial force.

Pb Reference atmospheric pressure of layer number b.

Pl Lateral force. p Internal pressure.

xvii pCL Classical buckling pressure.

R Ideal gas constant in J kg−1K−1; Launcher’s radius.

R∗ Ideal gas constant in Nm mol−1K−1

R⊕ Earth’s equatorial radius.

R1 First principal radius of curvature of a shell.

R2 Second principal radius of curvature of a shell.

Rb Base radius of a blunted cone.

Reff Effective Earth’s radius.

RF Fineness ratio.

Rint Interior radius in the case of a toroidal tank.

Rog Ogive radius.

Rt Tip radius of a blunted cone.

RFn Nose fineness ratio.

ReL Reynolds number. r Sum of Earth’s equatorial radius and the vehicle’s altitude.

S Sutherland constant.

Sbody Launch vehicle’s cylindrical part surface area.

Sell Ellipsoid surface area.

Snose Launch vehicle’s payload fairing surface area.

Sog Ogive surface area.

Sref Reference area.

Sw Wetted area.

SF Safety factor.

T Temperature; Thrust.

T∞ Exospheric temperature.

Tb Reference temperature of layer number b. t Thickness.

V Velocity.

xviii V1st First stage volume.

V2nd Second stage volume.

Vcone Volume of the conical payload fairing.

Vcyl Volume of the cylinder that inscribes the payload.

Vell Ellipsoid volume.

Vfuel Fuel tank volume.

Vog Ogive volume.

Vox Oxidizer tank volume.

Vprop Tank volume for a certain propellant. ve Exhaust velocity.

W Vehicle’s weight.

Wf Supported fluid’s weight.

Z Altitude

Zb Reference altitude of layer number b.

Subscripts

0 Sea-level reference value. b Number of atmospheric layer; Base drag. body Body section. c Subsonic compressive flow. f Friction drag. hs Hypersonic flow. l Laminar flow. nose Nose section. sb Subsonic flow. ss Supersonic flow. t Turbulent flow. ts Transonic flow. w Forepressure drag.

xix xx Acronyms

CFRP Carbon Fiber Reinforced Polymer

CRES Corrosion-Resistant Steel

DL Design Load

ESA European Space Agency

FOS Factor of Safety

FOSU Ultimate Factor of Safety

FOSY Yield Factor of Safety

KM Model Factor

KP Project Factor

LEO Low Earth Orbit

LH2 Liquid hydrogen

LL Limit Load

LOX Liquid oxygen

MMH Monomethyl-Hydrazine

N2O4 Nitrogen Tetroxide

NASA National Aeronautics and Space Administration

PMD Propellant Management Devices

RANS Reynolds-averaged Navier–Stokes equations

SCC Stress Corrosion Cracking

SFU Total Ultimate Safety Factor

SFY Total Yield Safety Factor

TRL Technology Readiness Level

UDMH Unsymmetrical Dimethyl-Hydrazine

xxi xxii Chapter 1

Introduction

”Earth is the cradle of humanity, but one cannot live in a cradle forever.” Konstantin Tsiolkovsky

Once believed to be inaccessible, space travel is becoming more and more enticing and appealing to a broader range of people. Year after year, the number of launches per year increases, edging closer the hundredth mark. To a large extent, this is owed to the fact that space exploration was once strictly the business of government funded enterprises, whereas now it has been opened up to private investors, which has significantly ramped up the competition. This of course means that each company strives very hard to reduce the cost of each mission and does so by improving the efficiency and capability of their technology. This market has opened up a large array of possibilities, seeing as any and every improvement comes as an opportunity. Omnidea, a Portuguese SME performing research in the aerospace and energy markets, picked up on one such opportunity and committed itself to investing on the very first Portuguese launch vehicle. The goal of this work is to perform a preliminary design of a micro launch vehicle, intended to carry 50 kg of payload to an altitude of 360 km and to be launched within the next 2 or 3 years. The main parameters to be defined are the materials, layout, structural sizing and structure-imposed limits.

1.1 Motivation

Starting with Konstantin Tsiolkovsky’s derivation of his famous equation in 1903 [1], followed a few decades later by Robert Goddard’s experiments with liquid-fuel rockets in 1926 [2], the technology uti- lized in launch vehicles has seen great developments and improvements. The first missiles were developed for war purposes by the Germans. This would become a noticeable trend throughout the twentieth century, especially so during the Cold War and the Space Race, when the Soviet Union and the United States strove hard to be the first to develop the technologies to place a man on the moon. One such technology was, of course, the launch vehicles, which accordingly saw a great boom in this time.

1 Today, however, a new era has been entered, one in which private companies and investors can, and do, provide their own launch services. They are increasingly able to compete with the government- backed agencies, such as NASA or ESA. Their collaboration has become so significant that it is now customary for the governmental institutions to elicit services from private companies. A very mediatic example of this was the contract celebrated between NASA and SpaceX. With so much space opening up for new players in this industry, Omnidea has decided to be one of them. There are various aerospace companies that are now focused on producing heavier launch vehicles, which can carry heavier payloads, their target being reaching new planets, such as Mars. At the same time, another sector is mainly interested on the nano-satellite industry: as of now, there are hundreds of nano-satellites orbiting our planet – generally referred to as CubeSats – and efforts are being made to increase their number. One way of sending these satellites into orbit is setting them as secondary payload – in other words, these satellites are not the main concern of the mission, that role being taken by the larger payloads. Consequently, this approach constrains the satellites’ orbit and restricts aspects such as launch sched- ules or the equipment they may have on-board. One alternative is building smaller launchers, which would be specifically designed for small pay- loads. This concept maximizes the revenue from the operation of a spacecraft, since it is possible to deliver it in a shorter time and to the desired orbit. This is what has been proposed by Omnidea, which aims to develop an affordable micro launcher. The feasibility of this project must be decided, and so a preliminary study of the various systems of a launch vehicle is currently being undertaken.

1.2 Topic Overview and Requirements

The various launch vehicles are traditionally divided into categories, according to the amount of mass that they can put in orbit. A small-lift launch vehicle is capable of putting up to 3 000 kg of payload into Low Earth Orbit (LEO), a medium-lift launch vehicle can carry 3 000 to 6 000 kg and a heavy-lift launch vehicle is able to take more than 6 000 kg [1]. There are two more categories that can be added: a super-heavy lift vehicle, capable of lifting more than 50 000 kg, and a micro launch vehicle, which has a maximum payload capability of 1 000 kg. It is this last type of vehicle that is the main focus of this work. Each vehicle comprises various subsystems, as the propulsion, the navigation, guidance and control, the communication and the structure and mechanisms subsystems. This work concerns the structure subsystem, more specifically its preliminary design and sizing. The main objective at any point of the project is to achieve the minimum structural mass possible, in order to either decrease the amount of propellants needed, or increase the payload capability of the launcher. This will lead to a decrease in the expenses regarding a launcher mission, which means an increase in the profit that the company can have. The first step is to define the vehicle’s functional requirements, by defining the target orbit and the payload mass. Next, the operational requirements, as number of stages, the velocity gain (∆v) bud- get, type of propulsion and an estimation of the dry mass must be established. This was prepared by

2 Omnidea and it was the basis for this study. As it was previously mentioned, the goal is to design a vehicle that can carry a payload of 50 kg to a Low Earth Orbit, more specifically to an altitude of 360 km. Regarding the operational requirements, the launcher will be composed of two stages, use liquid propulsion and its tanks will be internally pressurized to 0.5 MPa. About 7 engines are expected, 6 for the first stage, with a length of 0.6 m, and 1 for the second, with a length of 1 m, each weighing about 35 kg. The remaining relevant requirements are presented in Table 1.1.

Table 1.1: Operational requirements

Total ∆v 7 698.9 m/s First stage ∆v 3 444.7 m/s Second stage ∆v 4 254.2 m/s Total take-off mass 7 590 kg Total propellant mass 6 891 kg First stage propellant’s mass 6 000 kg Second stage propellant’s mass 891 kg First stage dry mass 600 kg Second stage dry mass 99 kg Isp 340 s

Figure 1.1 presents the variation with time of the total velocity and total mass of the vehicle, as estimated by Omnidea.

(a) Total velocity (b) Total mass

Figure 1.1: Velocity and mass variation with time.

1.3 Thesis Outline

When designing a launch vehicle, there are many variables that need to be accounted for. These are interconnected and as such they cannot be studied independently. The design is therefore an iterative process, consisting of various system loops. This work begins with a revision of the state of the art, regarding the suitable propellants and mate- rials for the vehicle. In the following chapter these are specified through trade-off studies, which allow a

3 comparison between the various alternatives and a more informed choice when picking the propellants and materials best suiting the requirements. After that, a new loop begins, one of structural design, in which the aim is to reach the lowest structural mass. In this case, an aerodynamic analysis is selected to determine the best fineness ratio, i.e., the best ratio between the vehicle’s length and its diameter. Finally, according to the external and internal mechanical loads, the dimensions of the main struc- tures of each stage are determined by a static structural analysis. The results are then compared to the initial dry mass estimation, to evaluate if a new iteration is needed, so the requirements are met.

4 Chapter 2

Bibliographic Revision

In this chapter, the state of the art is presented regarding the structural components of which a launch vehicle is composed, the elements of the propulsion subsystem that influence them and the available materials from which they can be manufactured.

2.1 Structural Components

The structural subsystem of a launch vehicle is composed of various structures: tanks, intertanks, interstages, skirts or other transition sections, fairings, payload fittings and adapters as well as the thrust frame. These are considered the primary structures [3] and will be the focus of this work. In this section, the various types of structures will be described and their past designs analysed. Figure 2.1 presents Ariane 5 as an example of a typical launch vehicle configuration.

Figure 2.1: Example of a launch vehicle’s structural components. Adapted from [4].

5 2.1.1 Tanks

The propellant tanks are one of the most important structural components of a launcher. When first approaching them, a distinction must be made between pressure vessels and pressurized structures. According to ISO 14623:2003 [5], a pressure vessel is “a container designed primarily for the storage of pressurized fluid that fulfils at least one of the following criteria:

a) contains gas or liquid with high energy level;

b) contains gas or liquid which will create a mishap (accident) if released;

c) contains gas or liquid with high pressure level.”

On the other hand, a pressurized structure is a structure that carries not only an internal pressure but also significant external loads [3]. In early designs the tanks were just pressure vessels with a surrounding external skin that supported the external loads. However, as the existence of this skin resulted in an increased mass, an undesirable outcome, there was a strong effort in the investigation, and subsequent development, of integral tanks. An integral tank is therefore considered a pressurized structure, having requirements different from those of simple pressure vessels, due to the highly variable flight loads it has to bear. There are three types of tanks that have been used to the present day: stable metal, balloon or composite tanks. Within the stable metal tanks, the most common configuration is a shell made of an aluminium alloy, usually stiffened by integrally machined stiffeners in an isogrid or orthogrid pattern [3]. The balloon tank is a very thin-wall type of structure which is not stable under the load of its own weight unless it is internally pressurized [3]. Although this configuration was a success in the Atlas launcher, the stable tanks are generally preferred because they facilitate their operation. Also, because of advancements in material engineering and design techniques, stable structures can now be produced with a weight which allows them to have a global competitive edge [6]. Finally, composite tanks offer a significant weight reduction, over the metal tanks, and are also more resistant to fatigue and flaw propagation. However, they have their own failure mechanisms, such as de-lamination [3]. Their advantages have led to an increasing effort in the development of composite materials. Regarding their geometric shape, the spherical geometry is the one which offers the best pressure vs mass efficient design. However, due to the large propellants’ mass requirements, either very large tanks are needed - leading to an inefficient shape, since a large radius leads to a large frontal area and thus, a high increase in drag [7] - or several smaller tanks properly arranged. Figure 2.2 presents a cross-section of the N1 Rocket, as an example of the use of spherical tanks. As a result, the most common solution is to design the tanks as a cylinder with two hemispherical heads. Depending of the specific needs of each launcher, the shape of the those heads can be adapted. For example, if space is more important than saving mass, a hemispherical head can be transformed into an ellipsoidal shape. This is done at the expense of increased weight: for the same volume, the flatter the heads, the higher the thickness needed, thus adding mass [7]. The three geometries are shown in Figure 2.3.

6 Figure 2.2: Example of spherical tanks: N1 Rocket. Reproduced from [8].

(a) Spherical (b) Cylindrical with hemispherical (c) Cylindrical with ellipsoidal heads heads

Figure 2.3: Possible tank geometric shapes. Adapted from [7].

Furthermore, in what concerns their configuration, there are also three possible architectures: cen- tral, toroidal or outcentered, which are represented in Figure 2.4. The central configuration consists in positioning the tanks in a central axis one above the other. In the toroidal solution one tank is toroidal and the other is cylindrical and coaxially positioned with the first and in the outcentered configuration the tanks are positioned around the longitudinal axis of the stage. Besides defining the tanks position, it must also be decided if the two tanks will be completely sep- arated or if they will have a common wall (common bulkhead tanks). This last option represents a reduction in the stage height and dry mass seeing as both tanks are sharing a wall. The choice of these architectures will be greatly influenced by the vehicle shape, so only after a preliminary decision of the vehicle’s layout is made, can the tanks size, shape and position be decided as well. Independently of their type, tanks are considered a thin-wall structure [9]. Therefore, the Membrane Theory can be used, i. e., it can be said that only the in-plane loading will be significant in the part of the structure far from attachments or other discontinuities [3].

7 Figure 2.4: Possible tank architectures. Reproduced from [1].

Concerning the stiffeners, there are various types that can be used, the main division being between integrally machined (isogrid or orthogrid) and mechanically attached stiffeners (columns and rings) [3]. When sizing the tanks, the total volume should be about 5-10% larger than the volume of needed propellants, to allow thermal expansion, or an even higher percentage if a pressurant gas needs to be stored inside the tank [9]. Also, if internal equipment, like anti-sloshing devices, needs to be added, its volume must also be considered [1].

2.1.2 Adapters

All the unpressurized structures used to connect the functional parts of the vehicle are consid- ered adapters. These include intertanks, interstages and skirts [3]. Figure 2.5 shows two examples of adapters, one from the Falcon 9 launch vehicle and the other from the Ariane 5.

(a) Falcon 9 composite interstage [10] (b) Ariane 5 vehicle equipment bay [11]

Figure 2.5: Adapter examples.

An adapter can have an exterior shell, its primary structure, and an interior secondary structure composed of shelves or brackets to support equipment like wires or guidance and navigation hardware [3]. The way composite materials are used in these components is similar to the way they are applied in the aircraft industry. However, due to the highly variable temperature at which the adapters are exposed, the low and high temperature behaviour of the materials will be more relevant than in the case of aircrafts, since they can be exposed to both the low temperatures of propellants, in case cryogenics are used, and the high temperatures in the atmospheric flight [3].

8 These components are usually cylindrical or conical - in case the two structures being connected have different diameters.

2.1.3 Payload Fairing and Nose Cones

These structures are the forward end of a launcher so they are usually conical or tapered shells, i.e., low drag bodies. In the case of launch vehicles, the nose cone usually has the purpose of protecting the payload, so it is called payload fairing. Figure 2.6 presents Falcon 9 and Ariane 5 fairings, as examples of typical constructions.

(a) Falcon 9 fairing [12] (b) Ariane 5 fairing [13]

Figure 2.6: Fairing examples.

During the atmospheric part of the flight the payload fairing will be subjected to high heat fluxes, so when choosing a material these temperature variations need to be taken into account. The payload protection and the low weight requirements have led to a common use of sandwich or stiffened shells designs [3]. From current designs it can be concluded that the cylindrical part of the fairing has usually a fineness ratio of at least 1 and that the conical/tapered part length is about 1 or 2 times the diameter [9].

2.1.4 Thrust Frame

The thrust frame is the structural part that supports the engine and connects it to the stage. It is also an important component to consider since it will transmit the thrust force from the engine to the vehicle. As the engines to be used are still not defined, the thrust frame cannot be designed yet, so it will not be part of this work. However, based on existing launch vehicles, it can be assumed that the thrust will be applied at the bottom of the tank’s walls, as shown in Figure 2.7.

9 (a) Thrust frame of a Titan’s launcher [14]. (b) Prototype of a Prometheus engine and thrust frame [15].

Figure 2.7: Thrust frame examples.

2.1.5 Secondary Structures

Structural elements like feedlines and pressure vessels, other than the main propellant tanks, are considered secondary structures. Feedlines, used to feed the propellants to the engine, are the longest and the largest lines and have the highest flow rates. Because these tubes need to form elbows and bend in some parts, the material needs to be formable. It also must be compatible with lubricants and the propellants. In addition, the corrosive and chemically active environment that these elements will endure can cause the fracture toughness of the material to decrease considerably [3].

An example of smaller lines are the pipes that connect the pumps to the engine, which are considered part of the propulsion subsystem [3]. In what concerns pressure vessels, as was mentioned before, they are used to store pressurant gases, hydraulic fluids and secondary propulsion or reaction control propellants [3].

It is possible to conclude that, in addition to the propellants volume and the loading requirements the vehicle has to meet, the composition of the propellants themselves will also play a major role in the sizing of the vehicle, due to their different densities and storage conditions. Therefore, Section 2.2 is dedicated to analysing the available propellants, so a proper structural sizing can be made.

2.2 Propulsion

The design of the vehicle’s tanks depends on many parameters, two of them being the propulsion and the propellant type. Until now, all launch vehicles have used chemical propulsion [6], and since this is the only technology mature enough to be readily used, so will this vehicle. Still, a decision must be made regarding which propellants will be used to meet the mission requirements. Only then can the sizing process begin, since the tanks volume and materials will vary significantly for each case.

10 2.2.1 Type of Propulsion

There are various types of propellants that can be used, being the main distinction between liquid and solid, which define the type of propulsion. A third type can also be included, which uses both liquid and solid propellants, named hybrid propulsion. As mentioned before, the decision between these three types was made by Omnidea, which chose liquid propulsion. The main reasons for this choice were: it is easier to control the trajectory, as the engines are easier to regulate, it is easier to develop the engines in a civil context, as the solid engines are considered explosives, and it has better performance (higher specific impulse). In addition, when using the same propulsion type for both stages, the engines of each stage can essentially be two versions of the same design, which reduces the development process needed. As the second stage engine needs to be reignited, which is not possible with solid propulsion, it is advantageous to choose liquid propulsion for the first stage as well. Regarding the liquid propellants, a division can be made between monopropellants - when there is only one propellant, stable in a determined environment but that can be made to decompose under pressure, heating or a through a catalyst - and bipropellants - when there are two distinct liquids, an oxidizer and a fuel, that react with each other [16]. They are first kept in tanks, then they are carried to the combustion chamber, where they decompose or combine, and finally the resulting products are expanded and accelerated through the nozzle. Figure 2.8 presents the typical configuration of a liquid rocket engine.

Figure 2.8: Schematics of a liquid rocket engine. Reproduced [16].

Another division exists between earth storable and cryogenic propellants. Earth storable propel- lants, as the name itself indicates, can be stored at ambient temperature and pressure conditions. The most common ones are kerosene fuel and hypergolic propellants such as nitrogen tetroxide (N2O4), monomethyl-hydrazine (MMH) or unsymmetrical dimethyl-hydrazine (UDMH). The term hypergolic means that the fuel and the oxidizer will spontaneously ignite upon contact or mixture [16]. In contrast, cryogenic propellants, such as liquid oxygen or liquid hydrogen, are liquefied fluids kept at very low temperature [16-100 K] and at ambient pressure [16], so they have to be loaded right before the launch or otherwise they will evaporate.

11 While the cryogenic propellants have a higher performance, they also present some challenges that make their operation more difficult than the earth storable liquids. Not only do they have lower density, which means that larger tank volume is required, thus increasing the tank’s weight, but they also require cooling of feedlines and engines so that instantaneous vaporization, which can lead to great losses, does not occur [1]. It is also important to keep the propellants at the lowest possible temperature to maintain their density and the boil-off rate at minimum levels [6].

In the specific case of liquid hydrogen, due to its high susceptibility to leakage, special leak checks need to be conducted. Moreover, cryogenics tend to accumulate ice on their lines, valves and tanks, due to the condensing of atmospheric moisture, which can result in the falling of ice sheets that can potentially damage sensitive components [6]. Another problem that derives from the condensing of the atmosphere is the formation of liquid air enriched with oxygen, which can be very hazardous. Finally, even with insulation the boil-off is unavoidable, leading to a limited operation time [1].

The performance varies largely not only according to the type of propellants used but also to the combination chosen. For instance, the pair liquid oxygen/liquid hydrogen has a different performance than the same oxidizer but combined with kerosene. Figure 2.9 presents a comparison between the performance of various propellants.

Figure 2.9: Comparison between theoretical Isp of various propellants. Reproduced from [17].

The most common cryogenic propellants used are the combination of liquid oxygen and liquid hydro- gen, as well as liquid oxygen with a highly refined form of kerosene, usually RP-1. Despite the latter not having a performance as high as the former pair, kerosene has a higher density than liquid hydrogen, which means a more reasonable tank size and weight, and that less insulation is required.

12 2.2.2 Feeding System

Another study that has to be made is regarding the propellant feed system. There are currently two types used: pressure-fed or pump-fed system, both presented in Figure 2.10.

Figure 2.10: Propulsion feed systems. Adapted from [18].

In the case of a pressure-fed system, the tanks are pressurized above the chamber pressure, thus creating a pressure differential that will force both the fuel and the oxidizer into the combustion chamber. Therefore, this type of system eliminates the need for pumps, resulting in a cheaper, more reliable and simpler solution. In order to keep the tanks at a constant pressure, the pressurization system must continuously feed the tanks with a pressurized gas to make up for the loss of propellant that is being fed to the engine [1]. It should be added that the stabilization of the structure by its pressurization was already demonstrated by many authors [19] and in many existing vehicles. Usually inert gases, gaseous combustion products and/or vaporized propellants are used as pressurants [1]. However, like all solutions, it also has some disadvantages. Since wall thickness is directly propor- tional to the internal pressure and tank size, should large tanks be needed, as in the case of cryogenic propellants, this solution can imply a considerable stage structural mass [1]. This limits the pressure range at which this system can be applied since higher pressures would imply heavy tanks [16]. It should be noted that, in order to produce a high level of thrust, resulting from a high exhaust velocity, the ratio between the combustion chamber pressure and the nozzle exit pressure should be the highest possible, leading to greater levels of pressurization required in the tanks, during the atmospheric flight phase. So, by limiting the pressure at which the system can work, the pressure-fed system will also be limiting the maximum thrust per mass of propellants used. This type of feeding system is therefore usual in small and upper stages, which operate with smaller tanks and lower atmospheric pressures, where the weight increase is not as problematic. When it comes to the pump-fed system, not only does it represent an increased complexity, due to its higher part count, but it also can cause a spontaneous vaporization of liquefied gases when they are exposed to the decreased pressure of the pump inlet. This leads to a phenomenon called cavitation, which can cause irreversible damage to the pump, when the originated bubbles implode and create

13 shock waves [1]. In order to minimize it, the propellants should be kept at a low temperature, in a compressed liquid state, to help prevent the instant vaporization, since the lower the temperature, the easier it is for a liquid fluid to maintain its liquid state when subjected to low pressures. The relative cold temperatures will also help to cool the combustion chamber. It is then possible to use this type of feeding system while keeping the tanks pressurized, thereby taking advantage of the structural stabilization provided by the internal pressure and of the possibility of feeding the propellants to the pump without the entrapment of vapour.

2.3 Materials in Launch Vehicles

There are various types of materials that can be used in launch vehicles, from metallic alloys to com- posites. Since it is important to comply with the low mass requirements while simultaneously supporting the mechanical and thermal loads resulting from the operation of the vehicle, the selection of these ma- terials is a process that must be done carefully. In fact, the sizing of the vehicle cannot be done without the prior selection of the materials [3].

Aluminium alloys

Aluminium is an abundant, light and corrosion resistant element [20] and, as of today, it is still the most common material found in aerospace structures [21]. Due to its low yield strength in its pure form, it is combined with other elements in order to have structural utility, thus resulting in aluminium alloys [20]. The properties of these final materials are dependent on the type and proportion of alloying elements and the method of fabrication [22]. Should the tank structures be welded, the weldability of an aluminium alloy becomes important. As it depends on many factors, such as the alloy’s composition, its hardness state and the welding process itself [22], it became an important field of research for the space industry. Nowadays, the use of friction welding facilitates the welding of these alloys [23]. The 2000-series aluminium alloys have been the most common choice for the propellants tanks [3]. Their principal alloying element is copper and they are strengthened by solution heat treatment and ageing, which results in a suitable strength even at cryogenic temperatures [22]. The percentage of copper can vary between 0.9% and 6.3% and elements like silicon and lithium are added to allow the room-temperature age hardening and to improve forgeability and strength. In addition, manganese, magnesium and titanium are also used in small quantities to refine the grain and to help prevent stress corrosion [3]. Within the 2000-series, the alloy 2219 is vastly used. It has adequate properties at cryogenic tem- peratures making it the usual choice for tanks [3] and it can also be used in elevated temperature applications (from 200oC to 315oC) [22]. For example, at liquid oxygen temperatures (90 K) the ultimate and yield strengths increase about 20% regarding room temperature, and at the liquid hydrogen tem- perature (20 K) that increase reaches 30% [3]. It has good machinability and, contrary to other alloys,

14 good weldability as well [24]. Another example of a widely used 2000-series alloy is the 2014, which only has 4.4% of copper against the 6.3% of the 2219. Both are easily machined thus allowing integrally machined stiffeners [3].

Other series, like the 7000, have higher strength but their poor weldability and sensitivity to notching at cryogenic temperatures prevents them from being used in tanks. Nonetheless, they are used at interstages and other structures not subjected to low temperatures [3]. Their main alloying component is zinc but they can also contain magnesium and copper [22].

Currently, the lighter aluminium-lithium (Al-Li) alloys are being used due to the weight reduction advantage. For example, with just 2 to 3% of lithium, the weight can be reduced approximately by 10% while increasing stiffness, leading to an effective reduction of 15% [23]. For instance, when compared to the 2219, the Al-Li alloy 2195 has a higher yield strength (about 20%) and is 8% stiffer, despite having a lower density, resulting in a lighter structure [3]. However, these alloys have some disadvantages, like reduced ductility, anisotropy of in-plane properties [24] and difficulty of acquisition.

In general, aluminium alloys have good machinability, they can be chemical milled (being this pro- cess an usual one, since it is an economical operation), and their properties are especially good in compressive designs [24]. The tensile strength can vary from 100 MPa to 800MPa and the average Young modulus is about 70 GPa. One problem with aluminium is that it corrodes when in contact with graphite fibers in an humid medium, since it creates a galvanic cell [25]. In case combined carbon fiber and aluminium structures are used, it is therefore necessary to electrically insulate both components.

Titanium

Along with aluminium, titanium can also be applied to the aerospace industry. It has a high strength- to-weight ratio, medium density, low coefficient of thermal expansion, as well as being resistant to cor- rosion and oxidation, and it can be further strengthened by alloying or heat treatment [22]. Also, it can withstand both cryogenic and high temperatures and has better compatibility with composites than aluminium [25]. However, due to its elevated initial cost (it can be 5 or 10 times more expensive than aluminium) as well as its machining cost (up to 1 order of magnitude higher than for aluminium) its use is still very limited [25].

Despite being easily welded either by fusion or solid-state techniques, the welding process needs to be done with an inert gas protection or in a vacuum, to prevent the embrittlement and other defects of the weld [26]. This is because titanium has a high affinity for oxygen, nitrogen and hydrogen, especially at high temperatures [22]. When it comes to its manufacturability, it is considered a difficult metal to machine, since it has poor thermal conductivity and a low elastic modulus, and easily becomes work- hardened, thus quickly wearing out the tools. Because of the residual tensile or compression stresses that are induced by this process, as well as possible defects, it usually requires surface treatments after machining [26].

15 Beryllium

Beryllium is another metal that presents good properties for aerospace applications. It is a lightweight material with high strength and moderate temperature capabilities, that can be hot shaped and formed at hight temperatures, machined and welded (although fusion welding is not recommended) [22]. Despite having good mechanical properties, its extreme toxicity leads to difficulties in processing and manufac- turing beryllium components [21], since expensive safety measures are required [3]. This in turn results in the loss of its advantages when compared to the simpler production of other metals, so beryllium is usually not chosen. Nonetheless, it can be machined to extremely close tolerances, making it a good choice when very narrow tolerances are required [24].

Nickel alloys

Inconel 718, Hastelloy and the A-286 alloy are designated as heat-resistant alloys; they are consid- ered superalloys [22]. For a structure with no external insulation, fit to withstand velocities up to Mach 5.5, these alloys are the practical choice [27]. However, they are heavy materials and since launch vehi- cles generally exceed that velocity level, external insulation is usually still required. They are commonly found in feedlines [3]. Inconel 718 is a vacuum-melted nickel-base alloy, which presents high resistance to creep and stress rupture and high strength at cryogenic temperatures [22]. It is one of the strongest materials at low temperatures and can be used up to 650 oC[28]. Hastelloy is generally used in parts that require resistance to oxidation and high strength above 780 oC. It is possible to machine them, with the use of high-power tools, and weld them (including fusion welding). The A-286 is an iron-chromium-nickel-base alloy, that has a reduced cost when compared with the other superalloys due to its iron content [22].

Steel alloys

Steel and its alloys are commonly used in pressure vessels [29], being one of their main advantages their wide range of mechanical properties, that can be obtained by choosing one of many combinations of alloy and heat treatment. According to [3], feedlines are mostly made of 321 or 347 Corrosion-Resistant Steels (CRES). These are austenitic stainless steel alloys and have good applicability on the aerospace industry, and more specifically in launch vehicle systems, because they possess advantageous cryogenic properties as well as good strength in high temperatures. Alloys such as the 301 and the 310 were already used in liquid oxygen tanks, in the Centaur stage of the Atlas launchers [28].

Composites

Composites are especially interesting due to their low density when compared to metals and their high strength. In fact, in the case of DC-XA’s liquid hydrogen tank, NASA has claimed a reduction of 37% in its mass when compared to the same metal tank previously constructed [3]. The other main

16 advantage of these materials is the ease in fabricating complex shapes, like thick curved structures, and the reduction of the manufacturing cost [30]. One type of composite application is the sandwich construction, commonly applied in the fairing. This construction consists of two parallel face sheets, usually of an aluminium alloy or a carbon fiber laminate, with an intermediate core [21]. However, within composites, the most common type used in space industry is the fiber composite. In order to take full advantage of the fiber-reinforced composites, usually multiple layers are combined, in which each layer is oriented in the direction that better fits the structural requirements. This is so because by varying fiber orientation and stacking sequences the structural properties will be significantly changed [30]. In light of this, high-modulus or high-tenacity carbon fibers combined with a thermosetting matrix are the basis of composite application in space [21]. However, the matrix will decrease the tensile strength of the composite, therefore adding weight while decreasing the advantages fibers present. Also, the thermoset matrices commonly used are brittle, which can lead to a brittle composite. A complication that arises from these materials is that the directional properties of the material are not readily available to use, which makes choosing them more difficult. Also troubling with laminates is the difficulty of joining various laminated panels and their low interlaminar strength [3]. In addition, when applied to pressurized structures subjected to compression loads, buckling becomes a concern, propitiated by geometric imperfections, which are difficult to control while manufacturing and challenging to screen in the inspection tests [3]. When dealing with composite tanks, reinforced joints will be in some cases required, leading to the loss of some advantage of composites when compared to metal tanks [3]. Regarding their compatibility with the propellants - which conditions their applicability to tanks - they require a protective liner inside the tanks to separate the propellant and the composites, due to the possibility of ignition, in the case of a oxidizer tank, compatibility issues and leakage prevention [3]. This increases the complexity of the manufacturing, since if the liner fails there is a risk of complete mission failure, as it happened in 2016 with SpaceX Falcon 9 vehicle. In this mission, the liquid oxygen infiltrated a buckle that existed in the composite overwrapped pressure vessel, which was located inside the liquid oxygen tank and contained helium, leading to the ignition of the material, thus causing catastrophic failure [31]. Regardless, composites can be easily applied in simpler structures like the payload fairing. For example, the Space Shuttle Orbiter nose cone was made of reinforced carbon/carbon which is a fibrous composite of graphite fibers and a pyrolytic graphite matrix, that can resist to temperatures up to 1900 K [3]. In general, composites are used due to their reduced weight and part count, improved structural and thermal performance and potentially total lower cost. However, they may present issues in grounding, shielding, handling damage, environmental interactions, non destructive inspection, full-scale test re- quirements, fracture control and compatible interfaces and attachments [32]. Since fiber composites are the most usual on the space industry, the commonly used fibers are next described. Glass Fibers These type of fibers have high strength, flexibility, stiffness and present good bulk properties as hardness and inertness [32]. Glass fibers can be used at very high temperatures because they do not

17 burn or support combustion and have excellent chemical resistance [33]. They are divided in various categories, as E-glass, ECR-glass or S-glass [32]. E-glass fibers are low-cost and general-purpose fibers and the most common type used. They have excellent electrical insulation properties [33]. On the other hand, there are the special-purpose fibers, as the high corrosion resistance (ECR) and the high strength (S) fibers, that were developed for specific applications, like the military industry. For example, the S-glass strength is 10 to 15% higher than that of E-glass and at the same time it can withstand higher temperatures [32].

Aramid fibers One of the main characteristics of aramid fibers is that they fail in a ductile, more benign manner, unlike the glass or carbon fibers [32]. They have high strength-to-weight ratio, thermal resistance (in- cluding to cryogenic temperatures) and toughness [33]. However, when in compression, they exhibit a nonlinear behaviour, resulting in buckling issues and limiting the application of these fibers when dealing with compressive or flexural loads [32]. Additionally, they can be difficult to cut due to their high tough- ness and must be protected from UV exposure by painting or coating [33].

Carbon fibers Like glass fibers, carbon fibers are also divided into multiple categories, as high tenacity (HT), high strength (HS), very high strength (VHS), high modulus (HM) or ultra high modulus (UHM) fibers [1]. These have complete elastic recovery upon unloading and are not affected by moisture or atmosphere oxidation at room temperature [32]. Oxidation does become a problem when the temperature is elevated, with the maximum temperature being around 350oC to 450 oC, for long exposure times [32]. However, at these temperatures the matrix has typically already failed so the composite material will not have a service temperature as high. The main mechanical properties that make carbon fibers a good choice for aerospace applications are the high elastic modulus, tensile strength and electrical/thermal conductivities [33]. Because carbon is a brittle material, and is combined with a usually brittle matrix, very high local stresses will appear in discontinuities, changes of section size or cracks, causing abrupt failure [33].

Carbon-Carbon composites Carbon-carbon composites can withstand very high temperatures (up to 2000 oC) without degrading their mechanical properties. In fact, an increase in the tensile strength as temperature rises is very common. However, above temperatures of about 350 oC they become susceptible to oxidation and therefore cannot be used for long periods in an oxygen rich and high temperature environment, unless a protective coating is applied [32]. Despite its high production costs, which makes C-C composites an expensive solution, it was still the material chosen for the nose cap and leading edges of the Space Shuttle [32].

18 Chapter 3

Trade-off Studies

With the various options described, for both propellants and materials, it is possible to do an analysis to choose which are the ones that best fit the requirements of this vehicle. This is done so by using trade-off studies, which are presented in this chapter. A comparison between the various propellant and material options is therefore made, before the structural analysis can be initiated. First the propellant combination is chosen and then the material for each structural element is defined.

3.1 Comparison of Propellants

According to [1], [6], [34], [35] and [36], a list with the ready to use propellant combinations and their characteristics was made and presented in Table 3.1. Omnidea has also enough knowledge about the liquid methane and liquid oxygen combination properties, so this combination was also considered.

Additionally, some parameters were chosen to make a comparison between the various options: specific impulse, tank structural mass, complexity, availability, safety, cost, boiling point and required insulation as well as reliability. These parameters are explained in Section 3.1.1, where a weight is attributed to each one. Finally, a score is given to each propellant combination, in each category and for each feeding system, and the one with the best score is chosen.

Table 3.1: Selected propellant combinations characteristics

Specific Impulse Specific Impulse Density Mixture Cost (1980-90) Freezing Point Boiling Point (Vac) [s] (SL) [s] [kg/m3] Ratio [$/kg] [oC] [oC] LOX / LH2 459 382 1140 / 71 5.50 0.08 / 3.60 -219 / -259 -183 / -253 LOX / Kerosene 352 292 1140 / 806 2.60 0.08 / 0.20 -219 / -73.0 -183 / 147 LOX / Methane 340 300 1140 / 423 3.00 0.08 / - -219 / -187 -183 / -162 N2O4 / Aerozine 50 338 292 1450 / 903 2.00 6.00 / - -11.0 / -7.00 21.0 / 70.0 N2O4 / MMH 336 288 1450 / 880 2.16 6.00 / 17.00 -11.0 / -52.0 21.0 / 87.0 N2O4 / UDMH 333 285 1450 / 793 2.61 6.00 / 24.00 -11.0 / -57.0 21.0 / 63.0

19 3.1.1 Propellants Selection Criteria

Specific Impulse

The specific impulse (Isp) is given by the exhaust velocity (ve), divided by the standard gravity (g0 = 9.81 m/s2), and is a common performance measure. Two values are given for each combination of propellants: vacuum and sea level. The sea level value will be used on the evaluation of the performance, since most of the flight will be atmospheric. In spite of the final performance also depending on the combustion efficiency of the engine, this is one of the most important parameters so a 25% weight was set to its relative importance. From Table 3.1 it is easy to compare the performance of each propellant combination and assign the scores.

Tanks Structural Mass Estimation

The tanks structural mass can be, in a first approximation, estimated using Mass Estimating Relations (MER’s) [37]. Knowing the operational requirements, presented in Table 1.1, the densities of the various fuels and oxidizers and their mixture ratios, i.e., the oxidizer to fuel ratios, the volume of the tanks can be computed using Equations (3.1) to (3.5).

Total Propellant Mass Fuel Mass = (3.1) Mixture Ratio + 1 Oxidizer Mass = Total Propellant Mass − Fuel Mass (3.2) Fuel Mass Fuel Volume = (3.3) Fuel Density Oxidizer Mass Oxidizer Volume = (3.4) Oxidizer Density Total Volume = Fuel Volume + Oxidizer Volume (3.5)

According to the MERs, it is then possible to estimate the tanks structural mass. For liquid hydrogen tanks: Tank’s Mass = 9.09 × Fuel Volume (3.6)

For other propellants:

Tank’s Mass = 12.16 × Fuel/Oxidizer Volume (3.7)

The final mass will be the sum of both tank’s mass. Dividing by the dry mass, given in Table 1.1, the ratio between the tanks weight and the dry mass of each stage is obtained. Along with the performance, this parameter is important since it represents the available mass for systems other than the structures. With this in mind, the weight attributed was again of 25%. Looking at Table 3.2, the scores regarding the tanks structural mass can directly be decided, taking into account that the pressure-fed system will result in heavier tanks, since they will require thicker walls.

20 Table 3.2: Tanks mass estimation results

First Stage Second Stage Tanks structural Tanks structural mass Tanks structural Tanks structural mass mass estimation [kg] to total dry mass ratio (%) mass estimation [kg] to total dry mass ratio (%) LOX / LH2 172 28.7 26 25.9 LOX / Kerosene 71 11.9 11 10.7 LOX / Methane 91 15.2 14 13.7 N2O4 / Aerozine 50 60 10.1 9 9.1 N2O4 / MMH 61 10.1 9 9.1 N2O4 / UDMH 62 10.3 9 9.3

Complexity

This is used to evaluate the complexity of the resulting system using each propellant. The cryogenic propellants will have a more complex system than the others because they require a low operational temperature, which can result in some problems as was explained in Section 2.2.1. In addition, the injector of hypergolics can be very simple and no igniter is needed.

Regarding the combination LOX/Methane, although it is a cryogenic one, both fuel and oxidizer have similar handling temperatures (90 K for LOX and 111 K for Methane) so the infrastructure used for the liquid oxygen can be adapted for the methane. On the contrary, the combination of LOX/Kerosene has very different handling temperatures, so two different handling methods have to be used. Furthermore, extra care is needed in the case of structural tanks to ensure that the LOX is not heated due to the heat transfer from the kerosene tank, since the materials commonly used are heat conductors, thus increasing the system complexity.

Finally, the pump-fed system will also represent an increase in complexity when compared to the pressure-fed one. Simplicity is a desirable characteristic of any system and will result in a more robust and cheaper design, therefore a weight of 10% was given here.

Availability

This parameter is related to the ease of acquisition of the propellants, i.e., if they can be easily obtained or not. An easy access represents a saving in total costs as it decreases the manufacturing and transport fees, so a 10% weight was chosen.

It was found that it is possible to commercially acquire LOX and LH2 from multiple suppliers in Portugal, making these two components the most available. Besides, the place from where the vehicle is expected to launch already has a LOX supply. Methane is also widely available and can be extracted from natural gas by a simple process. In contrast, the kerosene commonly used in launch vehicles is the RP-1 type, which is highly refined and used only for the space industry, therefore having a low supply, which is expected to be even further decreased in the future. In the case of the other propellants, they are chemical compounds that need to be fabricated and may require safety procedures owing to their toxic nature. Because all of the three hypergolic fuels are derivatives of hydrazine they are all given the same score.

21 Safety

Because some propellants are toxic, corrosive or known carcinogens, they represent greater risk and cost of handling, as well as an increase in environmental pollution, should any accident occur. This was given a 10% percentage because the risk and difficulty of handling can be very harmful to the mission.

The distinction is then made between toxic and non-toxic, i.e., if the propellants are toxic they are assigned with the lowest score, otherwise they get the highest.

Cost

When it comes to the cost, as it is difficult to find recent prices publicly available, the prices NASA was paying between 1980 and 1990 were used for this comparison, with the exception of methane. Because of environmental regulations, the prices presented in Table 3.1 for the hydrazine derivatives are higher than their production cost, due to their toxicity [38]. With the current environmental protection laws, it is expected that the fees for the toxic components will still be high, which makes these fuels and oxidizers more expensive.

In the case of methane, the price is about 1 Euro/kg [39], which is around 1.24 USD/kg. To be able to compare the various prices, the inflation rate was applied to update the 1990’s values. Then, using the price of each component and their mixture ratio, the final price per kg of each propellant combination was determined, and is presented in Table 3.3.

Table 3.3: Propellants cost

Propellant Cost [USD/kg] LOX / LH2 1.21 LOX / Kerosene 0.21 LOX / Methane 0.37 N2O4 / Aerozine 50 - N2O4 / MMH 18.48 N2O4 / UDMH 21.40

Despite prices being updated with the inflation rate, a direct comparison between them would not be adequate because there are other parameters that can greatly influence the price variation of the propellants, such as demand or even the environmental regulations. However, with extra care, these are useful to establish a comparative Likert scale. For example, with the low supply of RP-1 kerosene and its increasing demand, along with an expected further reduction in its availability, an increase in its price is predicted. In fact, in 2002 it was reported that its price was three times higher than that of methane, according to a non-disclosed company study.

This parameter was also given a 5% weight since it does not present any structural constraints and this is usually a small fraction of the total launch cost, which includes the vehicle, use of infrastructures and manpower required.

22 Boiling Point and Insulation

The boiling point was included in this analysis because it represents the ease of vaporization of the propellants. The higher the boiling temperature, the higher the propellant temperature allowed before it vaporizes. The boil-off rate is defined as the amount of mass that is lost due to vaporization, in a given time period. In the case of low boiling points, like the ones of cryogenics, the vaporization happens more easily so these propellants will be more prone to boil-off. In addition, in the case of a pump-fed system, the easier vaporization will favour the cavitation phenomenon. Insulation is related both to the boiling point of the propellant, and to the difference between the working temperatures of the fuel and the oxidizer (in the case of a common bulkhead tank or connected structural tanks). The lower the temperature required to maintain the propellant liquid is, the more in- sulation will be needed. In the case of a common tank wall, should the tanks be kept at considerably different temperatures, there also arises a need for extra insulation between them, resulting in an in- creased structural mass. Although the cryogenic propellants require more insulation due to their low working and boiling tem- peratures, hypergolic propellants will also need it to some extent, because the boiling point of the oxidiser N2O4 is also relatively low (21oC). Like the performance, the boiling point is also directly evaluated by the data presented in Table 3.1. Regarding the insulation needed in the tanks, the cryogenic propellants have a greater need than the others. As it was mentioned, the combination LOX/Methane does not require as much insulation as the LOX/LH2, since the temperatures of both fuel and oxidizer are similar, so little to no insulation is required between the tanks. The combination LOX/Kerosene, despite the kerosene not needing insulation, is still a semi-cryogenic mixture, so there is a temperature difference between the tanks. There is no significant distinction between the other combinations. These parameters combined will weigh 10%.

Reliability

To evaluate the reliability of the propellants, the failures of all the currently active launch vehicles were studied, to determine whether or not they were related to the propellants or the feed system (Ap- pendixA). However, the results, which are shown in Table 3.4, were inconclusive since some propellant combinations were used many more times than others, leading to an inadequate comparison. Based on this data, the Technology Readiness Level (TRL) was chosen to replace the reliability in the trade-off study, so a proper comparison could be made. The propellant combinations of which no information is available were removed from this analysis so the remaining all have maximum TRL, with the exception of methane, which does not have flight heritage. In the case of liquid methane, its TRL is 6 for the pump-fed system, since it has already been successfully used in hot fire tests, but 5 for the pressure-fed system, because these tests were conducted in smaller engines. This factor is important in the decision-making process, seeing as it influences the probability of failure. However, it was not considered a decisive one so a 5% weight was assigned.

23 Table 3.4: Reliability of each propellant combination

Feeding System Propellants Launches Reliability LOX/LH2 - - LOX/Kerosene - - LOX/Methane - - Pressure-Fed System N2O4/Aerozine 50 153 1 N2O4/MMH 6 1 N2O4/UDMH 7 1 LOX/LH2 396 0.992 LOX/Kerosene 2600 0.999 LOX/Methane - - Pump-Fed System N2O4/Aerozine 50 - - N2O4/MMH - - N2O4/UDMH 826 0.996

3.1.2 Propellant Selection

The last step of this process is to create the selection matrix, where each row represents a propel- lant combination, divided according to the feeding system, and each column a parameter used for the evaluation. The scores (from 1 to 5) are given in each category to each pair and, in the end, the total scores are determined using a weighted average and a combination chosen. The trade-off study results are shown in Table 3.5.

Table 3.5: Propellants selection matrix

Specific Tank structural Boiling point/ Final Complexity Availability Toxicity Cost TRL impulse mass Insulation Score Parameter Weight 0.25 0.25 0.1 0.1 0.1 0.05 0.1 0.05 LOX/Methane 4 2 3 5 5 5 2 2 3.35 Pressure fed N2O4/Aerozine 50 3 4 5 2 1 2 4 5 3.30 system N2O4/MMH 2 4 5 2 1 2 4 5 3.05 N2O4/UDMH 1 4 5 2 1 2 4 5 2.80 LOX/LH2 5 1 1 5 5 4 1 5 3.15 Pump fed LOX/Kerosene 3 4 3 3 5 3 3 5 3.55 system LOX/Methane 4 3 2 5 5 5 2 3 3.55 N2O4/UDMH 1 5 4 2 1 2 4 5 2.95

Looking at the matrix, it can be concluded that the combinations LOX/Kerosene and LOX/Methane with a pump fed system are the best options. As Omnidea is interested in exploring their own and new solution, and since this study has not excluded the LOX/Methane combination, this was the combination selected.

3.2 Comparison of Materials

The average properties of the commonly used materials that were described earlier are presented in Table 3.6[1, 22, 24, 28, 32, 33, 40]. With the exception of the carbon-carbon, for which no information was found regarding its fiber volume, the properties of the composites are presented, in each case, for an unidirectional laminate with an epoxy matrix and a 60% volume of the respective fiber.

24 Table 3.6: Properties of some commonly used materials

Tensile strength Elastic modulus Density Fracture toughness Thermal expansion Maximum service Material type √ [MPa] [GPa] [kg/m3] [MPa/ m] coefficient [10−6/K] temperature [oC] Aluminium Alloys 455-607 70 2750 20-31 23 200 Titanium Alloys 600-1000 100-125 4450 47-78 9 450 Beryllium Alloys ≈320 300 1860 172 11 600 Steel Alloys 515-1200 180-200 8000 30-140 16 850 Nickel Alloys 700-1500 190-215 8200 ≈100 15 800 Aramid fibers 3500 131 1400 1100 -2 440 Glass fibers 3320 79 1800 1700 3 970 HS carbon fibers ≈2100 120-150 1500 ≈4000 ≈0 2500 HM carbon fibers 1400-2300 >310 1600 ≈4000 ≈0 2500 Carbon-Carbon 200-260 90 1850 2500 1.1 2200

As it was done with the selection of propellants, the materials will be analysed and compared, using a set of parameters, to choose the ones that best fit the requirements of each structural component.

3.2.1 Materials Selection Criteria

The main characteristics that need to be considered during the selection process are: specific strength, stiffness, ease of manufacture, thermal properties, fracture and fatigue resistance, stress cor- rosion resistance and mechanical and chemical compatibility [3][21]. In addition, the cost will also play a role in the choice of the material. The various materials are next evaluated in each of these categories.

Specific Strength

Because a lighter structure is the ultimate goal, the specific strength of a material, which is the strength divided by the mass density, is of immense importance in the selection. Among metals, the best one is titanium, which means it can be used in locations where the strength is the main priority, like joints or areas of local load concentration [21]. Aluminium and beryllium alloys as well as composite materials also present good values.

Stiffness

The stiffness of a material represents the material’s ability to support loads without deforming, so it can be used to determine the buckling strength of a material [21]. In this case, both aluminium and titanium alloys have lower efficiency than steel or nickel alloys. Carbon fiber composites present the best results.

Manufacturability

There are some aspects of the manufacturability of particular significance when evaluating a material, like the weldability or machinability, ease of composite laminate making and the ease of assembly using fasteners, co-curing, adhesives or locking features [3]. Some materials will increase the difficulty of the manufacture process and will not allow an efficient shape or assembly, leading to the loss of the advantages that result from their intrinsic properties [3]. A simple and reliable manufacturing process

25 will reach a mature state faster, which leads to a cheaper fabrication of the structures and eliminates the need for fixing problems later in the vehicle assembly. Due to the low production scale of launch vehicle components, the raw material cost is in some cases small when compared to the production processes [3]. In other cases, and because a high quality needs to be assured and some of the materials are not used in any other applications, the raw material cost can be very significant. Nonetheless, as the cost of each material varies greatly with the intended amount, size and thickness of sheet or plate, at this point it is not possible to access this information, so only the influence of the manufacturability in the cost will be considered. Beryllium alloys, despite having a mass density comparable with that of composites and excellent mechanical properties (better stiffness than some carbon fibers), are problematic to process and manu- facture due to their extreme toxicity [1]. Recently there have been efforts towards using additive manufacturing to produce aerospace com- ponents. As reported in [41], stainless steels, titanium, titanium alloys and nickel alloys have been suc- cessfully used in this manufacturing process. For example, Inconel 718 has been used in gas turbines and Inconel 625 in gas turbine blades or heat exchangers.

Thermal properties

Thermal properties are important not only during service but also for the manufacturing processes, so they should be known in advance and compatible, not only with possible adjacent materials, but also with those processes [3]. Some of these properties are thermal conductivity, thermal expansion coefficient and the range of service temperatures. At low temperatures, an increase in the strength of a material as well as a decrease in its ductility are common phenomena. In contrast, at temperatures above room temperature one expects a decrease in the strength properties [22]. At cryogenic temperatures the properties will be strongly influenced by the crystal structure of the material. For example, the metals that are face-centered cubic, like aluminium, will experience a rise in their ultimate strength but not as much in the yield strength, thus preserving their ductility. On the other hand, body-centered cubic metals will experience the opposite: a greater increase in the yield stress than in the ultimate strength, leading to a more brittle behaviour [3]. Although the thermal properties must also be considered, they are not a decisive factor since the most commonly used materials have good thermal properties.

Fracture and fatigue resistance

Fatigue is the effect of repeated loads to which the material is subjected and it causes failure at stress levels lower than the design static stress. As launch vehicles are subjected to high vibration loads, resulting from the engines, supersonic atmospheric flight or even stage separation events, it is important to consider the fatigue that these vibrations will create. This criterion will also concern the sensitivity of a material to a small flaw. A brittle material is very sensitive to any crack or notch it may have, whereas a ductile material will endure the presence of a flaw

26 up until a certain load is reached, so it can be said to be more tolerant to small-scale damage. The fracture toughness of the material, which is a measure of its resistance to fracture, will also affect the fracture strength. This variable can also be interpreted as a measure of the tolerance or lack of sensitivity to flaws [22], and so will be used to evaluate the materials in this parameter.

Corrosion/Stress corrosion resistance

Because most bases from where vehicles are launched are in coastal regions, the environment the launcher will have to withstand while waiting for the departure is going to be salty and corrosive. Therefore, corrosion resistance is a desired property in the vehicle’s material. Stress Corrosion Cracking (SCC) is a form of localized corrosion and is defined as a subcritical crack growth phenomenon, caused by the presence of tensile stresses, a corrosive environment and the susceptibility of the material. It involves the crack initiation, propagation and consequent failure and is, therefore, considered a failure mechanism [42]. Tensile conditions can exist even while in storage, due to weight, residual stresses or joint assembly preload [21]. Due to its localized nature it is more difficult to detect than the more common uniform form of cor- rosion, and can be orders of magnitude greater than the last. The conditions that can cause SSC are usually known for each alloy and usually a change in at least one of the three necessary factors for its development is enough to either prevent or mitigate the phenomenon [42].

Mechanical and chemical compatibility

As it was explained before, there may be compatibility issues when aluminium comes in contact with carbon composites (galvanic corrosion), so this must be taken into account when choosing materials for components that will be in contact with each other. Also, the material susceptibility to oxygen embrittle- ment must also be evaluated, as well as its general compatibility with the propellants or other fluids, like lubricants or cleaning products.

3.2.2 Material Selection

During launch, the vehicle will endure several loads, from the axial thrust to the wind shear, acoustic loads, thermal loads or the mechanical vibration [6]. In addition, for the vehicle design, and consequently, for its material choice, other loads such as the ground transportation ones, propellants loading thermal conditions and ground wind loads occurring before launch must also be considered [43]. Therefore, amongst the criteria previously described, some will play a more important role than others in the decision, like the specific strength. Each structural component will have different material requirements, so they will be evaluated individually in the next sections. Since the launcher is meant to be built in the next 2/3 years, only materials with a high TRL in the space industry will be analysed for each case, as it represents less development time and lower costs in general. Therefore, the selected materials will have proven mechanical and chemical compatibility with the propellants.

27 The aluminium-lithium alloys will be excluded from this analysis because they are considered strate- gic materials and are particularly difficult to obtain.

Propellant Tanks

For the tanks material choice, the strength-to-density ratio will have a weight of 30%, since it repre- sents the most important required characteristic. The manufacturability will have an influence of 25%, because it directly impacts the cost, and the elastic modulus of 15% as it used to determine the buckling loads. The remaining properties will have a score of 10% since they will equally influence the material selection. In the case of structural tanks for cryogenic propellants, the only materials with high TRL are some aluminium and steel alloys. Table 3.7 presents their main characteristics [22, 24, 28].1

Table 3.7: Comparison of various aluminium and steel alloys properties at room temperature

Tensile Yield Elastic Strength-to-Density Fracture Thermal expansion Thermal Density Alloy strength strength modulus Ratio toughness coefficient conductivity [kg/m3] √ [MPa] [MPa] [GPa] [MPa ·m3/kg] [MPa/ m] [10−6/K] [W/m · oC] 2014 455 350 73 2800 0.16 24 23.0 160 Aluminium 2024 483 355 73 2780 0.17 37 23.2 155 alloys 2219 376 266 73 2840 0.13 39 22.3 135 A-301 515 205 193 8000 0.06 170 17.0 16.2 Steel A-310 515 205 200 8000 0.06 170 15.9 14.2 alloys A-321 515 205 193 8000 0.06 170 16.6 16.1

Looking at these properties it was possible to create the selection matrix, presented in Table 3.8.

Table 3.8: Decision matrix for the tanks material

Strength-to-Density Elastic Fracture Thermal Corrosion Manufacturability Total Ratio modulus toughness properties Alloy 0.3 0.15 0.1 0.1 0.1 0.25 1 2014 5 1 2 3 4 4 3.55 Aluminium 2024 5 2 3 3 4 4 3.80 alloys 2219 4 2 3 3 4 5 3.75 A-301 1 4 5 5 5 4 3.40 Steel A-310 1 5 5 5 5 4 3.55 alloys A-321 1 4 5 5 5 4 3.40

The material that will be used is therefore the 2024 aluminium alloy.

Adapters

Once again, only materials with high TRL will be considered.2 In this case, some aluminium alloys and some composites are eligible. Regarding the composites, as their characteristics vary significantly

1The fracture toughness of the steel alloys were averaged from results presented in [44] and [45]. 2In the case of the adapters, sandwich composites should be considered, namely a Carbon Fiber Reinforced Polymer (CFRP) sheet with an aluminium honeycomb core, now used in multiple launchers [4][46]. However, because their properties vary significantly with parameters such as sheet and core thickness or honeycomb cells size, and are not readily available, it is difficult to compare them with other materials.

28 with various factors, the average properties presented in Table 3.6 will be used. Table 3.9 presents the materials properties and Table 3.10 the matrix used to choose the adapter’s materials.3

Table 3.9: Comparison of various aluminium alloys and High-Strength composites properties at room temperature

Tensile Yield Elastic Strength-to-Density Fracture Thermal expansion Thermal Density Material strength strength modulus Ratio toughness coefficient conductivity [kg/m3] √ [MPa] [MPa] [GPa] [MPa ·m3/kg] [MPa/ m] [10−6/K] [W/m ·oC] Aluminium Alloy 7050 520 450 72 2830 0.18 31 24.1 157 Aluminium Alloy 7075 540 480 72 2810 0.19 ≈40 23.6 130 Aluminium Alloy 7175 510 440 72 2830 0.18 ≈40 23.0 - HS Carbon Composite 2100 - 120 1500 1.40 4000 ≈0 -

Table 3.10: Decision matrix for the adapters material

Strength-to-Density Elastic Fracture Thermal Material Corrosion Manufacturability Total Ratio modulus toughness properties 0.30 0.15 0.1 0.1 0.1 0.25 1 Aluminium Alloy 7050 3 3 3 3 4 5 3.60 Aluminium Alloy 7075 3 3 3 3 4 5 3.60 Aluminium Alloy 7175 3 3 3 3 4 5 3.60 HS Carbon Composite 5 5 5 5 5 4 4.75

As expected, when compatibility issues are out of the picture, a high-strength carbon composite is the best fit.

Payload fairing

In this case, the thermal properties must be considered more carefully, since it is the payload fairing that is going to experience the highest temperatures, apart from the engines and nearby structures. Because of this, the corrosion resistance, the manufacturability and the fracture toughness will only weigh 5% each and the thermal expansion will now weigh 25%. The materials to be considered are the same as for the adapters, so their properties are shown in Table 3.9. The selection matrix is presented in Table 3.11.

Table 3.11: Decision matrix for the payload fairing material

Strength-to-Density Elastic Fracture Thermal Material Corrosion Manufacturability Total Ratio modulus toughness properties 0.30 0.1 0.1 0.15 0.1 0.25 1 Aluminium Alloy 7050 3 3 3 3 4 5 3.60 Aluminium Alloy 7075 3 3 3 3 4 5 3.60 Aluminium Alloy 7175 3 3 3 3 4 5 3.60 HS Carbon Composite 5 5 5 5 5 4 4.75

Just as for the adapters, the best choice for the fairing is to use a High-Strength carbon fiber com- posite.

3An average fracture toughness of the 7000 series aluminium alloys was determined, according to the results presented in [47].

29 Table 3.12 summarizes the selected materials for each component.

Table 3.12: Selected material for each structural component

Structural component Material Propellant tanks 2024 Aluminium alloy Adapters High-Strength carbon fiber composite Payload Fairing High-Strength carbon fiber composite

30 Chapter 4

External Preliminary Sizing

In this chapter, the overall dimensions of the launch vehicle are determined. To do so, it is important to first establish an atmospheric model, so that the aerodynamic forces can be properly defined. From the various forces, the drag is the only whose determination is not immediate. Therefore, a large part of the chapter is dedicated to the calculations needed to predict it. Lastly, an overall preliminary sizing can be achieved, after comparing various possible fineness ratios and evaluating which one grants the lowest gravity and drag losses.

4.1 Atmospheric Model

To be able to determine variables such as the Mach number or the drag variation along the trajectory, due to the decrease of air density with altitude, it is important to establish an atmospheric model. There are various atmospheric models, such as the ”ISO Reference Atmospheres for Aerospace Use”, the ”ISO Standard Atmosphere”, the ”NASA/MSFC Global Reference Atmosphere Model (GRAM- 99)”, the ”COSPAR International Reference Atmosphere (CIRA)” and the ”U.S. Standard Atmosphere” [48]. All of them have something in common, namely the division of the atmosphere into different layers and regions according to their characteristics, resulting in different pressure, density and temperature variations with altitude. From these, only the ”GRAM-99”, the ”U.S. Standard Atmosphere” and the ”COSPAR International Reference Atmosphere (CIRA)” have the necessary altitude range, since they provide data at least up to 1000 km. Amongst them, the ”U.S. Standard Atmosphere” not only seems to be the most commonly used but also the easiest to compute since various linear expressions used for altitudes up to 86 km are presented. For higher altitudes, tables with analytical data that can be interpolated are provided. The 1976 version was chosen since it was an update on the first version from 1962 [49].

4.1.1 Temperature

The linear variation of temperature - valid up to 86 km and from 110 km to 120 km - is described by

31 T = Tb + Lb(Z − Zb), (4.1) where Lb is the temperature gradient, Tb is the reference temperature according to Zb, the reference altitude, and Z is the altitude being considered. The subscript b is the layer number, as presented in Table 4.1.

Table 4.1: Variation of Tb, Lb and Zb for each layer

Layer Reference Temperature Temperature Gradient Reference Altitude b Tb [K] Lb [K/km] Zb [km] 0 288.15 -6.5 0 1 216.65 0.0 11 2 216.65 1.0 20 3 228.65 2.8 32 4 270.65 0.0 47 5 270.65 -2.8 51 6 214.65 -2.0 71 7 186.87 0.0 86 9 240.00 12 110

Between 91 km and 110 km, the variation is described by the segment of an ellipse, as

" #1/2 Z − Z 2 T = T + A 1 − 8 , (4.2) C a where Z8=91 km, TC=263.1905 K, A=-76.3232 K and a=-19.9429 km. Finally, the last expression, describing the variation occurring between 120 km and 1000 km, has an exponential form,

T = T∞ − (T∞ − T10) exp (−λξ) , (4.3)

−1 where T10=360 K, T∞=1000 K, λ=L9/(T∞ − T10) = 0.01875 km , Z10=120 km, Reff is the effective

Earth’s radius and equals 6356.766 km and ξ is defined by (Z − Z10)(Reff + Z10)/(Reff + Z).

4.1.2 Pressure

There are two expressions describing the pressure variation with altitude, applicable from sea level up to 86 km. The first one, Equation (4.4), is applied when Lb is different from zero and the second one,

Equation (4.5), is used when Lb is zero.

g0M0   R∗L Tb b P = Pb (4.4) Tb + Lb(Z − Zb)

  −g0M0(Z − Zb) P = Pb exp ∗ (4.5) R Tb

The variables Tb and Lb are defined in Table 4.1 and Pb, which is the reference pressure, in Table 4.2.

32 2 ∗ As for the others, g0 is the sea-level value of the acceleration of gravity (9.80655 m/s ), R is the gas constant and equals 8.31432 Nm/(mol K) and M0 is the sea-level mean molecular mass for air (28.9644 kg/kmol) [49].

Table 4.2: Variation of Pb for each layer

Layer Reference Pressure b Pb [Pa] 0 101325.00 1 22632.10 2 5474.89 3 868.02 4 110.91 5 66.94 6 3.96

Above 86 km no simple expressions exist to describe the pressure variation so, with the data pre- sented in the tables available in [49], approximate polynomial equations were determined and are shown in Table 4.3.

Table 4.3: Air pressure variation for altitudes above 86 km

Altitude interval [km] Polynomial approximation 86 - 100 P = 4.8716264 × 10−6Z4 − 1.923518 × 10−3Z3 + 2.8554664 × 10−1Z2 − 18.89518106Z + 470.4392445 100 - 120 P = 2.1520000 × 10−7Z4 − 1.003800 × 10−4Z3 + 1.7582064 × 10−2Z2 − 1.370889320Z + 40.16030300 120 - 150 P = 2.7027270 × 10−9Z4 − 1.545088 × 10−6Z3 + 3.3209797 × 10−4Z2 − 3.183779000 × 10−2Z + 1.150336950 150 - 200 P = 3.9054170 × 10−11Z4 − 2.984560 × 10−8Z3 + 8.6124743 × 10−6Z2 − 1.115346000 × 10−3Z + 5.493320200 × 10−2 200 - 300 P = −5.4773400 × 10−13Z4 + 4.831869 × 10−10Z3 − 1.4566460 × 10−7Z2 + 1.587397100 × 10−5Z − 2.528022000 × 10−4 300 - 400 P = −1.0545460 × 10−7Z + 4.0026619 × 10−5

4.1.3 Density

There are also two expressions describing the density variation up to 86 km, presented in Equa- tion (4.6) and Equation (4.7), according to reference values (ρb), which are given in Table 4.4.

g0M0  1+ R∗L Tb b ρ = ρb (4.6) Tb + Lb(Z − Zb)

  −g0M0(Z − Zb) ρ = ρb exp ∗ (4.7) R Tb

33 Table 4.4: Variation of ρb for each layer

Layer Reference Density 3 b ρb [kg/m ] 0 1.225 1 0.36391 2 0.08803 3 0.01322 4 0.00143 5 0.00086 6 0.000064

Again, for altitudes above 86 km, the variation can be approximated by polynomial expressions, which are presented in Table 4.5.

Table 4.5: Air density variation for altitudes above 86 km

Altitude interval [km] Polynomial approximation 86 - 100 ρ = 9.437145 × 10−11Z4 − 3.715690 × 10−8Z3 + 5.5007421 × 10−6Z2 − 3.630175 × 10−4Z + 9.0146479 × 10−3 100 - 120 ρ = 4.236000 × 10−12Z4 − 1.969813 × 10−9Z3 + 3.4402350 × 10−7Z2 − 2.674972 × 10−5Z + 7.8151090 × 10−4 120 - 150 ρ = 4.741818 × 10−14Z4 − 2.687120 × 10−11Z3 + 5.7166112 × 10−9Z2 − 5.413566 × 10−7Z + 1.9266516 × 10−5 150 - 200 ρ = 2.258752 × 10−17Z4 − 2.252810 × 10−14Z3 + 8.3834740 × 10−12Z2 − 1.381516 × 10−9Z + 8.5267705 × 10−8 200 - 300 ρ = 3.389323 × 10−18Z4 − 3.737850 × 10−15Z3 + 1.5542610 × 10−12Z2 − 2.895930 × 10−10Z + 2.0482076 × 10−8 300 - 400 ρ = −2.40203 × 10−13Z + 9.026376 × 10−11

4.1.4 Mach number

Computing the equations previously presented, it is possible to determine the speed of sound, a, considering air as an ideal gas [49], as

p a = γRT , (4.8) where R is the gas constant and equals 287.0529 J/(kg K), T is the temperature and γ is the ratio of specific heats, which will be considered to have a constant value of 1.4. Knowing the velocity (V ) variation, which is one of the variables initially provided by Omnidea, and the speed of sound, it is possible to determine the Mach number, M, at each point of the trajectory, using Equation (4.9). The results are presented in Figure 4.1.

V M = (4.9) a

34 (a) Speed of sound variation (b) Mach number variation

Figure 4.1: Speed of sound and Mach number variation with altitude.

4.2 Rigid Body Forces

In this section, it is considered that the forces which will act on the launch vehicle are thrust (T ), gravity (W ) and drag (D). As the vehicle is not designed to withstand significant transverse aerodynamic loads, the angle of attack will be kept at, or very close to, zero, which means that it can be neglected [50]. Therefore, there will be no lift. Figure 4.2 presents the free-body diagram of the vehicle, during the vertical ascent phase.

Figure 4.2: Net force applied on the launch vehicle.

4.2.1 Thrust

A baseline launch profile was provided by Omnidea and is the basis of the sizing. The thrust and the acceleration profiles are presented in Figure 4.3.

35 (a) Thrust (b) Acceleration

Figure 4.3: Thrust and vertical acceleration variation with time.

4.2.2 Drag Force

One of the biggest constraints when it comes to sizing the launcher is the drag force it will have to endure. It is a key parameter for the analysis of the vehicle’s performance: since the energy loss due to drag can only be overcome by spending extra fuel, it should be built for minimum drag [51]. According to [52], there are two types of drag that have to be considered for a launch vehicle: friction and pressure drag. The latter is then divided into base and forepressure (or nose-wave [50]). Friction drag (Df) is caused by the viscous forces that act tangential to the body surface, whereas base drag (Db) and forepressure drag (Dw) are the result of pressure forces acting normal to the base and to the nose- cone, respectively. Since friction drag depends on the total length of the moving body, and pressure drag depends on the frontal area, with a constant volume, trying to decrease one will result in an increase of the other, so a compromise between the two must be found. The total drag will be the sum of the various drag components, as

D = Df + Db + Dw. (4.10)

However, the data and the expressions available to determine the drag are related to the drag coefficient

CD, so this coefficient must be later transformed into the drag force, using

1 D = C ρV 2S , (4.11) 2 D ref where Sref is the reference area, which for solids of revolution is usually the maximum cross-sectional area [53], ρ is the air density and V the velocity. As long as all the drag components are related to the same reference area, they can be combined to yield the total drag [50].

Friction Drag

Skin-friction drag is the consequence of a shear stress being applied on the surface of the launcher, due to velocity gradients in the boundary layer, and whose magnitude depends on the transition from laminar to turbulent flow. That being said, the friction drag will be dependent on the Reynolds number

36 as well as on the Mach number [50]. The Mach number was already determined for each instant of the

flight trajectory and the Reynolds (ReL) is calculated with

ρV L Re = , (4.12) L µ where L represents a characteristic length of the body (the total length of the vehicle, from its nose to its base, is considered to be sufficiently accurate for launch vehicles [50]) and µ the dynamic viscosity, here determined with Sutherland’s empirical law, given by [54]

3   2 T Tref + S µ = µref , (4.13) Tref T + S

−5 where µref = µ0 is 1.7894·10 Pa · s, Tref = T0 is 288.15 K and S is the Sutherland constant, equal to 110.4 K [49]. According to [52], the skin friction drag coefficient is given by

  Sw CDf = Cf , (4.14) Sref where Cf is the skin friction coefficient, usually given for a flat plate, Sw the wetted area and Sref the reference area. Looking at Figure 4.4, it is possible to define the reference area as well as the nose and body wetted areas of the vehicle, as [55]

Swn = 0.75πdLnose (4.15) Swb = πdLbody

2 Sref = πd /4.

Figure 4.4: Launch vehicle scheme. Adapted from [55].

The mean friction-drag for a cone or a cylinder can be related to that of a flat plate in the following √ manner: for a cone it is about 2/ 3 times bigger than the flat plate value [56] and for the cylinder it is approximately 15% bigger [50]. Making the appropriate changes to Equation (4.14), the final expressions to compute the friction drag coefficient are obtained,

  √ Sw CDf = 2 3 × Cf , cone (4.16) Sref

  Sw CDf = 1.15 × Cf , cylinder (4.17) Sref

37 The friction drag will also depend on the velocity regime of the vehicle. There are five flow regimes [57]:

• Subsonic incompressible flow if M < 0.3;

• Subsonic compressible flow if 0.3 < M < 1.0;

• Transonic flow if 0.8 < M < 1.2;

• Supersonic flow if 1 < M < 5;

• Hypersonic if M > 5.

For subsonic incompressible flow, the laminar drag coefficient is directly given by the Blasius solution for laminar flow over a flat plate [54], as

1.328 CD = √ , (4.18) fl ReL

5 which is valid if ReL < 5 × 10 , since above this value the boundary layer first becomes transitional, and then fully turbulent [52]. Because no good theory exists to model the transitional region, it will be considered that above this Reynolds value the boundary layer will be fully turbulent. Despite the previous equation being generally accepted for laminar flow, in the case of the turbulent skin friction coefficient there are various expressions provided by different authors [55]. One of them is the Karman-Schoenherr expression, which is ±2% accurate,

1 ≡ 4.13 log(Re C ). (4.19) p L ft Cft As this expression requires an iterative solution, a simpler model can be used, the Prandtl-Schlichting model, that is ±3% accurate,

0.455 C ≡ . ft 2.58 (4.20) (log ReL) Additionally, according to [52] there is a third equation derived by Hama, that agrees with the Karman- Schoenherr expression within ±2%, given by

1 C = . ft 2 (4.21) (3.46 log ReL − 5.6) Equation (4.20) and Equation (4.21) were both computed for M=0.2 and the results obtained are presented in Figure 4.5. Comparing the two results, the Hama model was chosen since it represents the worst case, i. e., the highest friction drag. Moving on to the subsonic but compressible flow, Barrowman [52] states that the laminar friction coefficient remains the same and that the turbulent one is given by

C = C (1 − 0.12M 2). (4.22) fct ft

However, Krasnov [58] reports that the laminar coefficient is given by

38 Figure 4.5: Comparison between the two models for the turbulent friction coefficient.

2 − 1 C = C (1 + 0.03M ) 3 (4.23) fcl fl and the turbulent by

2 − 1 C = C (1 + 0.12M ) 2 . (4.24) fct ft

In this case, both models could be chosen since they do not display significant differences between each other, as seen in Figure 4.6.

Figure 4.6: Comparison between the two models for the compressible friction coefficients.

Regarding the supersonic flow, for the laminar skin-friction coefficient the equation by A. D. Young (Equation (4.25)) is recommended [56] and for the turbulent skin-friction the Van Driest formula (Equa- tion (4.26)) is considered to be one of the most reliable [59].

ω−1 h γ−1 1 i 2
2 2 1.328 1 + 0.730 2 P r M C = √ (4.25) fssl ReL

− 1 sin−1 λ  γ − 1  2 0.242 1 + 2ω  γ − 1  1 + M 2 = log(C Re ) − log 1 + M 2 (4.26) q fsst L λ 2 C 2 2 fsst

In these equations γ = 1.4 is the ratio of specific heats, ω = 0.76 is the exponential factor in the empirical

39 expression of viscosity, P r = 1.0 is the Prandtl number and λ is given by [56]

1 λ = 1 . (4.27) h 2 i 2 (γ−1)M 2 + 1

Finally, for hypersonic velocities the friction drag is negligible since the flow is considered inviscid [57].

Base Drag

The base drag coefficient is related to the base pressure ratio, and thus to the base-pressure co- C efficient pb , which is caused by the negative pressure differential at the base [59]. Consequently, the base drag will be influenced by the properties of the airstream approaching the base as well as by the geometry of the base. In addition, the rocket exhaust streams will mix with the airstream, adding to the complexity of the calculations [50]. Because there is insufficient experimental data accounting for all the necessary parameters, the rocket exhaust will be neglected for this preliminary analysis. The base drag coefficient is considered to be symmetric to the base-pressure coefficient [50], whose variation with Mach number is presented in Figure 4.7.

Figure 4.7: Base drag coefficient variation with Mach number. Adapted from [59].

The expressions describing that variation are

3 −4 CDb = 0.115 + (10M − 2) × 10 , 0 ≤ M < 1

CDb = 0.255 − 0.135 ln M, 1.1 ≤ M ≤ 5 (4.28) 0.1 C = 0.019 − 0.012(M − 5) + , M > 5. Db M

According to [59], these expressions are only valid for a body of revolution, non-boattailed and lacking fins, as well as for a Reynolds number high enough to ensure a turbulent layer over most of the body length, so that the variation of the drag is approximately invariable with Reynolds number. Also, the fineness ratio should be higher than 5. Barrowman also presents his equations for base drag, for a body of revolution, as [52]

40 0.029 C = , 0 ≤ M < 0.3 Db p CDf 0.029 C = , 0.3 ≤ M < 1 Db q C (1 − M 2) Dfc

C = C∗ [0.88 + 0.12e−3.58(M−1)], 1 ≤ M ≤ M (4.29) Db Db cr 0.7 C = , M > M Db M 2 cr 0.892 With C∗ = 0.185 and M = = 2.074. Db cr q C∗ Db

The two models were compared for each regime and Figure 4.8 presents the comparison for subsonic velocities.

(a) Mach 0.2 (b) Mach 0.4

Figure 4.8: Comparison between the two base drag models for subsonic velocities.

Since the second model represents the worst case, it was chosen for this regime. However, varying the two models with the Mach number, instead of the body length, as is shown in Figure 4.9, it is possible to observe that, for a Mach number higher than 0.9, the Barrowman’s model starts to yield very high coefficient values. These values are significantly above what is expected for a drag coefficient, and so it is concluded that this model is not valid in this interval, and the first model will be used instead. In the case of the supersonic regime, the Barrowman’s expressions, whose results are presented in

Figure 4.9: Comparison between the two base drag models for Mach numbers between 0.3 and 1.

41 Figure 4.10, are an approximation of data provided by experiments done with a finned body. In Table 4.6 it is possible to compare the two models for various Mach numbers.

Figure 4.10: Base drag variation of a body of revolution according to Barrowman. Adapted from [52].

Table 4.6: Results of the comparison between the two base drag models for supersonic velocities

Model First Model CDb Barrowman Model CDb Mach 1.1 0.24 0.18 Mach 2 0.16 0.16 Mach 4 0.07 0.04 Mach 5 0.04 0.03

As it is shown, the first model presents higher values for base drag while being consistent with Figure 4.7. On the contrary, the Barrowman’s results are not in total agreement with Figure 4.10, which means that the expressions do not approximate well the actual base drag coefficient variation for a non- finned body. The first model was therefore chosen in this case, as well as for the hypersonic regime, since the Barrowman’s model does not account for these velocities [52].

Forepressure Drag

Forepressure drag is the second component of pressure drag. It is commonly named “wave drag” but since it is negligible in the mid-body section (cylindrical section), it is simply called forepressure or nose wave drag, as only the nose will have any influence. This component is therefore greatly influenced by the nose fineness ratio (RFn ) and shape, so it is common to use shapes like cones or ogives to minimize the drag. It also depends on the Mach number, rapidly increasing when velocities approach Mach 1 to later decrease after the transonic region ends [50]. Although the commonly used shapes have a sharp point, they can be blunted to facilitate manufactur- ing, detach the shockwave from the body - which helps to avoid high localized heating - and increase the resistance to handling and flight damage, as well as safety. The rounding of the nose cone is quantified by a bluffness ratio, which is the ratio between the tip and the base diameters [60]. As long as the nose length is constant, the tip blunting can even lead to a reduction of the drag [50]. The typical maximum level of bluffness ratio is 0.2 with the optimum value being around 0.15 [60]. For simplicity purposes and

42 for an initial analysis, a cone can be considered for the launcher’s nose, with a sharp tip that can later be blunted. For a slender shape, like the cone, the forepressure drag coefficient can be neglected for Mach numbers up to 0.9 [50]. According to [50] the nose wave drag coefficient can be estimated using

A CD = , 0.9 < M < 1.2 wts (R )2 Fn (4.30) 2 A =CDw (RFn ) ,

with A being determined by Figure 4.11, and RFn the ratio between the nose length Ln and its base diameter d.

Figure 4.11: Forepressure drag for transonic speeds. Adapted from [50].

The graphic was divided in four regions: one for X < −1, another from X ≤ −1 to X < 0, another 2 from X ≤ 0 to X < 4.5 and finally for X ≥ 4.5, being X equal to (M − 1)(RFn ) . Then, each region was approximated by an appropriate expression, as

A = 0.019X + 0.11, X < −1

A = 0.4X2 + 0.8X + 0.5, −1 ≤ X < 0 (4.31) A = −0.00319X4 + 0.03556X3 − 0.17593X2 + 0.47728X + 0.50143, 0 ≤ X < 4.5

A = 1.01,X ≥ 4.5.

For the supersonic regime the calculations are similar, but using Figure 4.12 and Equation (4.32) instead.

A C = , 1.2 < M < 5 Dwss 2 M (4.32) 2 A =M CDw

43 Figure 4.12: Forepressure drag for supersonic speeds. Adapted from [50].

This time the graphic was approximated by just one expression, as

M X = R Fn (4.33) A = 0.22764X4 − 1.20314X3 + 2.63294X2 − 1.31362X + 0.375.

For the hypersonic regime, the Newtonian Impact Theory can be applied [53]. For a cone of semiver- tex angle θc, the nose wave drag is given by [57]

2 C = 2 sin θc. (4.34) Dwhs

If the cone is then blunted, the wave drag can be computed using [57]

 2 2 Rt 4 CDw = 2 sin θc + cos θc, (4.35) hs Rb where Rt is the tip radius and Rb is the base radius. However, for blunted bodies the Modified Newtonian Theory is more accurate so it should be used instead [57],

"  2  2# 1 Rt 4 2 Rt CD = (2 − ε) (1 − sin θc) + sin θc − sin θc cos θc whs 2 R R b b (4.36) γ − 1 ε = . γ + 1

All the expressions that will be used to determine the drag force are summarized in Table 4.7.

44 Table 4.7: Expressions to be used to determine the drag force coefficients

Coefficient Flow regime Expression to be used Equation number

 −1 1.328 Sw Subsonic incompressible - laminar Cf = √ · Equation (4.18) l ReL Sref 1 Subsonic incompressible - turbulent Cf = 2 Equation (4.21) t (3.46 log ReL−5.6) Subsonic compressible - laminar C = C Equation (4.18) fcl fl 2 Subsonic compressible - turbulent Cf = Cf (1 − 0.12M ) Equation (4.22) Skin friction ct t ω−1 h 1 i 2 1.328 1+0.730( γ−1 )P r 2 M 2 √ 2 Supersonic - laminar Cfss = Equation (4.25) l ReL

−1 − 1 sin λ 1 + γ−1 M 2
2 √0.242 λ 2 Cf Supersonic - turbulent sst Equation (4.26) = log(C Re ) − 1+2ω log 1 + γ−1 M 2
fsst L 2 2

0.029 Subsonic incompressible CDb = q Equation (4.29) sb CD fsb C = 0.029 Subsonic compressible Db q 2 Equation (4.29) sb CD (1−M ) fc Transonic C = 0.115 + (10M − 2)3 × 10−4 Equation (4.28) Base drag Dts Supersonic C = 0.255 − 0.135 ln M Equation (4.28) Dbss 0.1 Hypersonic CD = 0.019 − 0.012(M − 5) + Equation (4.28) bhs M

A Transonic C = 2 Equation (4.30) Dwts (fn) Supersonic C = A Equation (4.32) Forepressure drag Dwss M 2 2 Hypersonic C = 2 sin θc Equation (4.34) Dwhs

4.2.3 Gravity Force

According to Newton’s Law of Universal Gravitation, the gravity acceleration at any altitude from Earth is given by

GM g = , (4.37) r2

where G=6.673 × 10−11 m3 kg−1 s−2 is the gravitational constant, M is the product of Earth’s mass 24 M⊕=5.9723 × 10 kg and the vehicle’s mass mtotal, and r is the sum of the Earth’s radius R⊕=6378.137 km (here considered the equatorial radius) and the altitude of the vehicle [61]. The gravity force depends both on the gravity acceleration and the vehicle’s mass, which is in turn influenced by its fineness ra- tio. For the preliminary assessment of the launcher sizing, both cylindrical and conical sections are considered thin-walled shells. Therefore, the total mass is given by the sum of Equation (4.38) and Equation (4.40) results, as well as the propellants mass, as presented in Equation (4.42). Henceforth, the cylindrical section will be named “body section” and the conical one “nose section”. In this case, it is important to consider that the tanks will not be fully cylindrical: at this point, it is admitted that they are composed of a cylindrical central part and two hemispherical heads.

45 mbody = (ρm · t · Sbody) · Mbody + Me (4.38)

2 Sbody = 2πR · [(Lb − 8R) + 8R ] (4.39)

mnose = (ρm · t · Snose) · Mnose + MP (4.40)

p 2 2 Snose = 2πR Ln + R (4.41)

mtotal = mbody + mnose + mpropellant (4.42)

In these equations, Mbody is a margin applied to the body’s mass and has two different values: the first one is 1.5 and represents the structural connections, thermal insulation, ducts and other structures, whereas the second one is just 1.3 and it is lower because it is applied only to the second stage, after the first is ejected, so the interstage does not need to be accounted for any more [1]. Mnose is 1.15 and represents cables, avionics and fittings as well as thermal insulation. As for the Sbody and the Snose, they represent the surface areas of the cylindrical and conical sections, respectively. MP represents the payload’s mass (50 kg), Me is the engines’ mass (35 kg each, for a total of 7) and ρm is the respective material density. In the end, the gravity force, or the vehicle’s weight, at any point of the trajectory, is given by

W = mtotal · g (4.43)

4.3 Launcher Preliminary Sizing

The first step in the preliminary sizing process is to assess any constraints related to manufacturing, logistics and ground operations. In this case, there is one operational constraint, related to the transport of the vehicle, since Omnidea has decided that it is going to be transported to its launch site inside containers, by ship. Therefore, each of the stages separately need to fit in 40’ intermodal containers, whose standard dimensions are approximately 3.4 m in width, 12 m in length and 2.4 m in height. Considering a lengthwise margin of 0.5 m in each side, for packaging and support, the length is then limited to 11 m and the diameter to 1.4 m. The overall vehicle sizing process begins with defining the internal volume of the tanks as well as of the payload fairing. The tanks volume can be determined using Equations (3.1) to (3.5) and Table 3.1, for the mixture LOX/Methane. The results of those equations are presented in Table 4.8. A margin of 15% was added in the end, to allow thermal expansion and extra space for internal equipment (see Section 2.1.1). Next, the payload fairing volume has to be computed. Since the data provided by Omnidea regard- ing the payload concerned only its mass, research was conducted about previously launched small payloads. Because the sampling was small, a margin was added to the results, as presented in Ta- ble 4.9.

46 Table 4.8: Total volume of propellant tanks

First stage tanks Second stage tanks Tanks total volume [m3] Oxidizer volume [m3] 3.95 0.59 4.54 Fuel volume [m3] 3.55 0.53 4.08 Total volume [m3] 7.50 1.12 8.62 Margin 15% Final volume [m3] 8.63 1.29 9.92

Table 4.9: Small satellites characteristics

Dimensions Mass Volume Base area Volume equivalent Base area equivalent Satellite [m × m × m] [kg] [m3] [m2] to 50 kg [m3] to 50 kg [m2] CYGNSS [62] 0.51 × 0.59 × 0.22 30 0.066 0.30 0.11 0.50 DUTHSat [63] 0.1 × 0.1 × 0.2 2 0.002 0.01 0.05 0.25 EcAMSat [64] 0.3 × 0.2 × 0.1 10.4 0.006 0.06 0.03 0.29 Hodoyoshi-1 [65] 0.503 × 0.524 × 0.524 60 0.138 0.26 0.12 0.22 GRUS [66] 0.6 × 0.6 × 0.8 100 0.288 0.36 0.14 0.18 WNISAT-1R [67] 0.524 × 0.524 × 0.507 43 0.139 0.27 0.16 0.32 Average volume [m3] 0.1 Average base area [m2] 0.3 Margin 20% Final volume [m3] 0.12 Final base area [m2] 0.36

With the payload volume determined, it is possible to compute the payload fairing size. It is con- sidered that the payload is a prism but inscribed in a cylinder, for packaging purposes, as shown in Figure 4.13.

(a) Prism (b) Prism inscribed in a cylinder

Figure 4.13: Payload configuration.

Knowing the volume and base area, the variables a, b and c can be determined, using Equation (4.44).

   a × b × c = 0.12 0.36c = 0.12 c = 0.33 ⇔ √ ⇔ (4.44) a × b = 0.36 a = b = 0.36 a = b = 0.60

From these values it is possible to determine the diameter of the cylinder, that will be given by √ a2 + b2, and its height, which is c. Finally, a relation between the cylinder and the nose-cone volumes must be determined. This is accomplished by using the geometrical similarity of triangles, as presented

47 in Figure 4.14 and Equation (4.45).

Figure 4.14: Illustration of the geometrical similarity of triangles.

(R − r)L c = n R (4.45)  L  L V = πr2c = πr2 (R − r) n = πr2L − πr3 n cyl R n R

Differentiating this equation with respect to the radius, the maximum volume of a cylinder that can fit inside the cone is computed as

dV L 2 cyl = 2πrL − 3πr2 n = 0 ⇒ r = R. (4.46) dr n R 3

And, from Equation (4.45), c = Ln/3. Comparing the volumes of the cone and the cylinder, it is observed that the nose-cone volume must be at least 2.25 times bigger than the cylinder’s one. The total nose- cone volume is finally given by

2 V π 2 R
1 L 4 cyl = 3 3 n = 2 1 Vcone πR Ln 3 9 √ !2 a2 + b2 (4.47) V =π c = 0.19 m3 cyl 2

3 Vcone = 2.25Vcyl = 2.25 × 0.192 = 0.42 m .

At this point, the propellant tanks and the payload fairing volumes are known. Considering the length of the engines, which is 1 m for the second stage engine and 0.6 m for the first stage engines, it is finally possible to size the vehicle. To do this, the ideal fineness ratio must be determined.

Ideal Fineness Ratio

It is expected that the ideal fineness ratio will be different for different phases of the trajectory. For example, during lift-off, as the velocity is very low, the main concern is the vehicle’s mass, so the best ratio is the one that leads to the lowest mass. However, as velocity increases, so does the drag force,

48 which also has to be taken into consideration. The best fineness ratio is the one that results in the best relation between the weight and the drag force. In this phase of the project, the structural stability does not need to be included, as it can be consid- ered that the buckling will be insensitive to the length. Therefore, the fineness ratio will be determined based on the mass and on the aerodynamic analysis of the vehicle, choosing the one that results in the lightest vehicle and in the lowest gravity and drag losses. These losses can be determined using [68]

Z tf W Z tf ∆vW = sin ϕ dt = g sin ϕ dt (4.48) t0 m t0 and Z tf D ∆vD = dt, (4.49) t0 m where ∆vW represents the gravity losses, ∆vD the drag losses and ϕ the flight path angle, which is the angle between the velocity vector and the local horizon. The sizing begins with the study of the second stage by itself, since only after that can the entire vehicle be analysed, up to the moment when the first stage separates. The radius is considered constant for the entire vehicle, for various reasons. If the second stage radius was smaller, it could lead to the appearance of a second shock wave at the connection of the stages. In addition, although the frontal area of this stage would decrease, and so its pressure drag, its wet area would increase, which would result in a higher friction drag. In the end, this configuration could possibly lead to an increase in the total drag. Moreover, using the same radius allows an equal design for both stages, which results in an easier and cheaper manufacturing process. This is commonly found in missiles and small launchers such as the Electron by Rocket Lab or the Russian Rockot. The fineness ratio is thus limited to 14.6, since there is a maximum length for the first stage (11 m). Ratios from 2 to 14.6 were therefore chosen and the expressions presented in Section 4.2 computed for each one. To estimate the mass of each stage, the densities of the 2024 aluminium alloy and of the High Strength carbon composite are considered. The thickness is determined using Equation (4.50) for the cylindrical parts and Equation (4.51) for the spherical ones. These expressions relate the internal pressure (p), the radius (R) and the admissible stress, in this case the yield stress (σy), with the thickness and will be later explained in Chapter5. The thickness is limited to a minimum value of 1 mm, since it is considered the minimum that can be manufactured.

pR t = (4.50) σy

pR t = (4.51) 2σy

To determine the dimensions of the vehicle, a tank geometry must be considered. Two cylindrical tanks with spherical tops and a common bulkhead are used for fineness ratios above 8. For smaller values, a spherical tank is used for the second stage since the radius increases significantly. Finally, for a fineness ratio of 2, two spherical tanks, one for each stage, are considered.

49 To calculate the propellant mass resulting of each fineness ratio, the total velocity change that needs to be produced (∆vthrust) must be first determined,

∆vthrust = ∆veff + ∆vW + ∆vD, (4.52) where ∆veff is the effective velocity gain that the vehicle needs to reach orbit. Knowing, from the initial inputs that were provided by Omnidea, that the first stage is ejected at an altitude of about 163 km, the drag losses can be neglected when studying the second stage by itself. Starting the analysis of the second stage, using Equation (4.48), it is concluded that the gravity losses are about 2511.6 m/s. Then, with Equation (4.53), named the Tsiolkovski equation, it is possible to determine the mass of propellant needed to achieve the required velocity [1],

mi ve ln = ∆vthrust, (4.53) mf where ve is the exhaust velocity, mi is the initial mass and mf the final mass. As the final mass of the stage will be its dry mass (structural mass, payload mass and one engine’s mass), it is possible to determine the total mass at each instant, up to its initial value. Then, the propellant mass is simply the difference between the initial and the dry mass. The results are presented in Table 4.10.

Table 4.10: Propellant and structural mass of the second stage for each fineness ratio

Fineness ratio Thickness [mm] Dry mass [kg] Propellant mass required [kg] 14.6 1 134.1 906.8 12 1 135.0 913.1 10 1 136.4 922.5 8 1 139.0 938.9 6 1 163.1 1103.2 4 1 199.9 1352.2 2 1 278.8 1885.4

Although the spherical tanks are usually lighter, cylindrical walls are required around them, adding mass. In addition, the surface area of the spherical hemispheres increases with R2, so as the radius increases, i.e., the fineness ratio decreases, the total dry mass of the stage increases as well. Analysing the first stage, the increase in its mass would be even higher, since the higher the radius the higher the drag losses, so more propellant mass would be needed to achieve the same velocity. It can therefore be concluded that the best fineness ratio is the maximum one. Looking at Table 4.10, it can be observed that the initial estimation of the stage’s dry mass - 99 kg - is lower than the calculated here - 134.1 kg. A new iteration is therefore needed, with a new input for the dry mass, so the correct volume needed to support the propellants can be determined. Similarly, due to the increase of the second stage total mass, the first stage propellants’ mass will increase as well, since the total supported mass will be higher. Consequently, the required volume for the first stage tanks will increase, which will lead to the decrease of the fineness ratio: for the constant maximum length, increasing the volume means increasing the radius.

50 Figure 4.15: Iterative process to determine the volume requirements of the vehicle.

In order to prevent a large number of iterations, a margin is applied in each case. For example, in the first iteration, instead of using the calculated value of 906.8 kg of propellants, 1000 kg are considered. Figure 4.15 describes the iterative process and presents the various results obtained before the final values were determined. As expected, it can be observed that the fineness ratio decreased from 14.6 to 12.7. These final results yield the dimensions presented in Table 4.11.

Table 4.11: Dimensions of the launch vehicle

Vehicle section FR Length [m] Radius [m] Diameter [m] Launch Vehicle 12.7 15.0 0.59 1.18 First stage 9.3 11.0 0.59 1.18 Second stage 3.4 4.0 (2.8+1.20) 0.59 1.18

Finally, for aerodynamic reasons, a change will be made to the design: the cone will be substituted by an ogive, more specifically, a tangent ogive. This is one of the most common nose shapes in launch vehicles and is formed by a segment of a circle, with its dimensions being defined in a way so it allows the vehicle body and its nose to be tangent, thus resulting in better aerodynamic characteristics [60]. Figure 4.16 represents a tangent ogive and Equation (4.54) presents the relation between the ogive radius (Rog) and its length and base radius [60].

R2 + L2 R = n (4.54) og 2R

Keeping the same dimensions of the nose-cone, the ogive radius will be Rog = 1.5 m. The volume is then given by [60]

 3   2 Ln 2 −1 Ln 3 Vog = π LnRog − − (Rog − R)Rog sin = 0.72 m . (4.55) 3 Rog

51 Figure 4.16: Scheme of a tangent ogive. Adapted from [60].

The surface area can be determined by the Theorem of Pappus-Guldinus [69], as [60]

q 2 2 y = Rog − (x − Ln) + (R − Rog) " # Z Ln q R2   (4.56) 2 2 og −1 Ln 2 Sog = 2πy dx = πLn Rog − Ln + sin + 2(R − Rog) = 3.05 m . 0 Ln Rog

These changes represent an increase of 70% in the volume available for the payload and a decrease of around 30% in the fairing’s structural mass, for the same wall thickness and material. Another possi- bility would be to keep the same volume, by decreasing the length to approximately 0.6 m, which would allow a saving of 64% in mass. However, this would result in a length smaller than the diameter and consequently in worse aerodynamic properties, so the first option was chosen. Figure 4.17 presents the launch vehicle’s general dimensions.

Figure 4.17: Launch vehicle overall dimensions diagram (in meters).

52 Chapter 5

Structural sizing

Before the sizing of each component can be done, the tanks’ architecture must be defined. In Sec- tion 2.1 various possibilities were presented, but with the length and radius of the stages being defined, it is possible to exclude some configurations, as the outcentered one, since the vehicle will be too narrow for them. In the next sections, the tanks’ components will first be defined and then sized according to the loading cases, using analytical expressions. Finally, a numerical analysis will be performed and the results compared to the analytical ones.

5.1 Tanks’ Architecture

The first step in the definition of the tanks geometry is to establish the propellants position. In a central configuration, for stability reasons, it is desirable to put the heaviest propellant on top of the other [1]. In addition, the coldest one should also be on top, so it is further away from the engines. In the special case of a bulkhead, there is one additional advantage in putting the coldest on top, since the other propellant, after evaporating, will hit the colder bulkhead and condensate again. This means that while on the launch pad, the evaporation is only of the colder propellant, which is advantageous in this case since only oxygen and not flammable gas would be vented. It can also be beneficial to put the smaller tank under the larger one, so the feedlines are smaller. In the case of this vehicle, there is no significant difference in the tanks size, since despite the mass ratio being of 3:1 (for each kg of methane 3 kg of oxygen are needed), the oxygen has a much higher density. As the oxygen tank will be both heavier and colder, it will be placed atop the fuel one. In Chapter4 it was considered that the tanks’ geometry consisted in a cylinder with spherical ends and a common bulkhead dividing them. However, this is not the only possible configuration. To choose from the various options, a trade-off study is again used. The parameters used in the evaluation are: structural mass, packaging efficiency, ease of installation of ducts and lines, ease of insulation, ease of fabrication and handling as well as the quantity of trapped propellants [7][40]. The available options are: a central configuration with two cylinders and ellipsoidal tops, a central

53 configuration with one cylinder with spherical tops and a bulkhead or a toroidal configuration with two cylinders, as presented in Figure 5.1.

(a) (b) (c)

Figure 5.1: Possible tank geometric configurations.

It can be seen that there are two possible options for the bulkhead. A flat bulkhead could also be an alternative. However, it presents various disadvantages, as the lack of a point for optimum placement of the tank’s outlet and the generation of a vortex at that location, which results in a significant quantity of trapped propellant. In addition, this would be the less mass-efficient solution, since the plate would need to be thicker than a hemispherical or ellipsoidal bulkhead [70]. This option was therefore discarded. The two suitable options also have advantages and disadvantages. When it comes to the placement of the outlet, a concave bulkhead will have the same problem as a flat one, and some propellant will be trapped as well [70]. Additionally, as the bulkhead will have to support the oxidizer weight, even if the pressure on both tanks is equal, there will be a compressive force on its top, which can lead to buckling. Finally, it would result in a smaller height margin between the fuel surface and the beginning of the bulkhead. In the case of a convex bulkhead, there is an optimum placement of the outlet, at its bottom center, which results in practically no trapped fuel. Also, when both tanks are at the same pressure, the oxidizer weight will cause a tensile stress, which is more beneficial than a compressive one, as it does not cause buckling. Looking at the advantages and disadvantages of both options, the one that performs best is the convex bulkhead, so it was the chosen geometry. Table 5.1 presents the volume of propellants, as determined in the last chapter, which is needed to define the tanks configuration. These values are then increased by 15% to yield the tanks required volume.

Table 5.1: Total volume of propellants

First stage Second stage Total volume Oxidizer volume [m3] 4.93 0.64 5.57 Fuel volume [m3] 4.43 0.57 5.00 Total volume [m3] 9.36 1.21 10.57

The first parameter to be used in the decision process, the structural mass, is the most important parameter in the design, so it will be given a 30% weight. The calculations regarding the second stage tanks are presented in AppendixB and the results are summarized in Table 5.2.

54 Table 5.2: Structural mass of each configuration type

Architecture Mass [kg] Separate tanks 25.6 Common bulkhead tank 22.1 Toroidal tanks 31

It is possible to conclude that the most mass efficient architecture is the central one with a bulkhead (Figure 5.1b). Regarding the manufacturing of the tanks, it is expected that the more parts in the tank, the more complex its fabrication and assembly will be. However, there is not much past experience in the manu- facture of toroidal tanks, as usually the preference has been over spherical or cylindrical ones (separated or with bulkheads) [7]. Adding to that, it is expected that the fabrication of two connected and concentric cylinders will be a complex process. This parameter will not only influence the difficulty of manufacturing the tanks but also their cost, as more complex processes will lead to more expensive results. Therefore, it will also weigh 30%. In what concerns the packaging efficiency, the two separated tanks have the worst. The common bulkhead configuration presents good packaging, since it takes maximum advantage of the available space. However, using the toroidal configuration the stage length could be decreased, so it is this con- figuration that presents the best packaging, as it would take practically all the space available. Figure 5.2 presents the different arrangements inside the second stage. This factor will also be of significant im- portance since it is not desired or beneficial to waste space that could potentially be used, for example, for avionics equipment. As a result, this is given a 15% weight.

Figure 5.2: Packaging of each tank configuration.

To evaluate the ease of installation of ducts, it is necessary to first define the location of the propellant feedlines as they can either be external or internal. In the case of external lines, although they are a simpler solution, they are exposed to the external load environment, thus requiring a more careful sizing process, as well as extra insulation, meaning a heavier solution. In addition, they will increase the cross-section area, which increases the total drag, and will result in the loss of symmetry, due to the preferential roll angle that will exist if the feedlines are not properly arranged around the vehicle. The internal feedlines, despite being more mass-efficient, mean an increased complexity in the design and manufacturing processes, since there will be a need of drilling holes in the lower tank and/or in the

55 bulkhead, which will influence the welding procedures, for example. However, the increase in complexity is not significant, contrary to the increase in drag, so internal feedlines were considered a more suitable option. With internal feedlines, the first and second cases present more difficulties in the installation, because if any leakage occurs in the bulkhead or the top wall of the lower tank, it can lead to mixing of propellants, which can cause an explosion and consequent loss of the vehicle. The third case is the most favourable, as the lines of each tank can directly be connected from their base to the engines. This parameter is given a weight of 10%. The insulation of the tanks must also be taken into consideration. Looking to Figure 5.2, it is possible to verify that the first case presents the best option. As the tanks are not in contact, there is only a need for exterior insulation. In the second case, the common wall may also need to be insulated. This can be done before the assembly so it is not expected that it will present great complexity. On the other hand, the third configuration requires insulation in the totality of its surface area, which results not only in an increase of mass, but also in increased complexity. This factor is also considered to have a 10% influence on the final choice. Finally, regarding the quantity of trapped propellant, neither of the three options present any con- straints so it will only be given a 5% weight. Table 5.3 presents the results of the trade-off study, including the six criteria just described.

Table 5.3: Trade-off study results for the second stage tanks configuration

Mass Packaging Ducts and lines Ease of Trapped Configuration Manufacturability efficiency efficiency installation insulation propellants 0.3 0.3 0.15 0.1 0.1 0.05 1.0 Separate cylinders with 2 3 1 2 3 3 2.30 ellipsoid heads Cylinder with spherical heads 3 2 2 1 2 3 2.35 and a bulkhead Toroidal cylinders with 1 2 3 3 1 3 1.90 ellipsoid heads

It is concluded that the best option is a central cylinder with spherical tops and a bulkhead. With this configuration, the tanks can be structural, i.e., instead of being a simple pressure vessel, the cylindrical part will be a pressurized structure (Section 2.1). With the calculations presented in AppendixB it was possible to determine the main dimensions of the second stage, which are shown in Figure 5.3. Regarding the first stage, as its available space is also constrained, the available configuration op- tions are the same as for the second stage, so the results of a trade-off study would be the same. The first stage will therefore be composed of an integral cylindrical tank with spherical tops and, in this case, a spherical bulkhead. Using the same expressions as for the second stage, the dimensions can be determined. The results are presented in Figure 5.4.

56 Figure 5.3: Second stage tanks configuration and main dimensions (in meters).

Figure 5.4: First stage tanks configuration and main dimensions (in meters).

5.2 Structural Loading

Having defined the overall dimensions of the main components of the tanks, it is necessary to define the critical loading cases that will dictate the last part of the sizing process.

During its flight, the launcher will be subjected to various types of loading, amongst which the most important for the preliminary design are thrust, weight and drag. In addition, the pressurized structures have to support the internal pressure. The other loads, as the wind, acoustic or thermal loads and mechanical vibrations require a more detailed analysis and will be considered in a future design iteration.

For design purposes the longitudinal acceleration imposed by the propulsion system can be consid- ered as statically applied, and so a static structural analysis will be conducted with the maximum values of each load being applied [71].

There are two critical events during the vehicle’s flight: the first is right before the launch itself, when the inertial force is maximum, and the second is after the speed of sound is reached, when the drag force increases sharply and so does the compressive force applied on the vehicle’s structure.

57 5.2.1 Lift-off

As it was said, at lift-off the inertial load is maximum, since the mass is at its maximum. This first case is described by

ma = T − W ⇔ T = W + ma = m(g + a). (5.1)

At this point, from Figure 4.3, the thrust is 153.3 kN, g is 9.80 m/s2 and the total mass is the initial mass, which is estimated to be 9190 kg using Equation (4.42) and considering the results presented in Figure 4.15. This results in an acceleration a of 16.7 m/s2.

5.2.2 Maximum Drag

When the vehicle reaches supersonic velocities, the drag force rapidly increases to a maximum value. Despite the thrust and weight decrease with time, this case, described by Equation (5.2), should also be analysed since the sum of the forces will be significant.

ma = T − W − D ⇔ T = ma + W + D = m(a + g) + D (5.2)

In Figure 5.5, it is possible to observe the variation of the total reaction force with altitude, and consequently with time, and conclude that there is a second peak in that force at an altitude of 5.7 km, which corresponds to a Mach number of 1.2.

Figure 5.5: Net force variation with altitude.

The drag force is determined with the expressions presented in Section 4.2.2 for a supersonic flow, which result in a force of 49.8 kN. However, since those expressions are approximations, some theoret- ical and others experimental, it is useful to compare the analytical results with numerical ones. There are various models that can be used to model the flow around the vehicle, but nowadays the majority of fluid computations are based on the Reynolds-Averaged Navier-Stokes (RANS) equations, which are divided according to the number of additional transport equations that need to be solved at the same time [72]. Within this category, the most common are the 2-equations models, like the k- or

58 the k-ω [73]. The most widely used model is the k-, that combines the convective and diffusive effects of transport of the turbulence properties but whose results fail in situations of adverse pressure gradient [72]. This limitation has lead to the development of other models, as the k-ω, which is currently the second most used [73]. Using ANSYS Fluent, a computational fluid dynamics software, and the k-ω model, a drag force of 45.6 kN was determined. It can therefore be concluded that the numerical result is a good approximation of the analytical one, with the relative error being around 8%. Figure 5.6 presents the results obtained using the k-ω model, where it is possible to observe the formation of shock waves. The pressure variation is shown in the top half and the Mach number in the lower half.

Figure 5.6: Pressure and velocity variation at M=1.2.

So at 5.7 km of altitude, the Mach number is 1.2, T is 131.9 kN, the total mass m is approximately 7333 kg so a is 17.98 m/s2, g is 9.78 m/s2 and the drag is maximum, with D=49.8 kN. With the critical loading defined, it is possible to start sizing the various components of the vehicle.

5.3 Analytical Method

The main structures of the vehicle are considered thin-walled shells, which means that they are defined by their thickness, that is small when compared to the other dimensions, and by a middle surface, which bisects the thickness [74]. The stresses in these shells are usually analysed according to the Membrane Theory, i.e., away from the ends where they are connected with other elements, the bending can be neglected and the only forces to support the external loads are the membrane ones [74]. Additionally, as the analytical expressions are theoretical approximations to the real case, the recom- mendations presented in various standards should be included in the sizing of the launch vehicle, since they correlate the theoretical expressions with experimental results. Presently, there are efforts being made to create new and updated standards, but in the meanwhile it is the NASA SP set of documents that is commonly used. In this case, the NASA SP-8007 and the NASA SP-8032 should specifically be used, since they concern the buckling of thin-walled circular cylinders and doubly curved thin-walled shells, respectively [75][76].

59 Both standards relate their expressions with the classical critical buckling stress, σCL, given by [74]

1 Et σCL = , (5.3) p3(1 − ν2) R where E is the Young Modulus, t is the thickness, ν is the Poisson ratio and R is the shell radius. Finally, and according to ESA guidelines [77], a factor of safety (FOS) must be applied to the sizing loads, along with a project factor (KP ) and a model factor (KM), whose typical values are presented in Table 5.4.

Table 5.4: Safety, project and model factors typical values

Factor Value FOSY 1.1 to 1.25 FOSU 1.25 to 1.5 KP 1.0 to 1.3 KM 1.0 to 1.1

The factors have the following definition [77]:

• “FOSY ensures an acceptable risk of yielding at limit load level during flight.”

• “FOSU is the key factor ensuring structural reliability objective is satisfied.”

• “KP accounts for possible mass increase at the start of launcher element design.”

• “KM accounts for the incertitude at the start of launcher element design with respect to mathemat- ical model used to establish the design.”

Figure 5.7 illustrates the development approach used for each structural component of the vehicle.

Figure 5.7: Development approach for each structural element. Reproduced from [77].

The limit load (LL) is the maximum load to be encountered in service [77], considering all expected load events, which multiplied by the design factors (KP and KM) yields the design load (DL). The total yield safety factor (SFY ) will be the product of FOSY , KP and KM and, in the same way, the ultimate safety factor (SFU) is obtained multiplying FOSU, KP and KM. The design and safety factors can be decreased as the project matures [78] but in the first iteration their maximum value should be used. Regarding the application of the factors, it is recommended that the mechanical loads are divided into two types: destabilizing loads that can lead to buckling, such as compressive loads or external pressure, and stabilizing loads which increase the apparent stiffness of the structure, such as tensile loads or

60 internal pressure. Then, the safety factor should only be applied to the destabilizing loads, keeping the stabilizing ones at their limit value [78]. The expressions derived from the Membrane Theory for each component will be presented in the next section.

5.3.1 Shells of Revolution

A shell of revolution is obtained by rotating a curve about an axis, which is named a meridian. Therefore, a shell element can be defined by two coordinates: the angle θ which is the angular distance that identifies a meridian and the angle φ, between a normal to the shell and its axis of revolution [79].

Therefore, the membrane stresses to be determined are the meridian σφ and the circumferential (hoop)

σθ stresses. Figure 5.8 presents a shell element, with the respective angles and forces.

Figure 5.8: Ilustration of a shell element. Reproduced from [79].

Ogival shell

The fairing nose is an ogival shell, which is considered a pointed shell, i.e., the meridian does not meet the axis of the shell at a right angle. For the case where it supports its own weight, the stresses are determined using [79]

qR (cos φ − cosφ) − (φ − φ ) sin φ σ = − og 0 0 0 φ t (sin φ − sin φ ) sin φ 0 (5.4) qRog σθ = − [(φ − φ0) sin φ0 − (cos φ0 − cosφ) + (sin φ − sin φ0) cos φ sin φ], t sin2 φ where Rog is the ogive radius and the angles φ and φ0 are defined as shown in Figure 5.9.

Ellipsoidal shell

The second stage bulkhead is an ellipsoidal shell and so its expressions will be different from those for the first stage bulkhead. There are three loading cases that need to be studied: when both parts of

61 Figure 5.9: Ogival shell. Adapted from [79].

the tank are pressurized, when only the upper part is pressurized and finally when only the lower part is pressurized. It is assumed that the second and third hypotheses can only exist before launch, so the only acceleration applied in those cases is that of gravity. The three cases can therefore be described by the applied pressure: no pressurization, internal pressurization and external pressurization. Before the expressions are presented, it is necessary to define the principal radii of curvature of the ellipsoid, based on the semi-axis (a and b), as [74]

a2b2 R = 1 2 3 (a2 sin φ + b2 cos2 φ) 2 a2 R = (5.5) 2 2 1 (a2 sin φ + b2 cos2 φ) 2 .

So at the bottom of the ellipsoid where φ = 180o, the radii are the same and equal to a2/b and at the o 2 edge, for φ = 90 , R1 = b /a and R2 = a. The stresses due to the various loading sources can now be determined. When supporting an internal pressure, the stresses are [74][80]

pR σ = 2 φ 2t  2  (5.6) p R2 σθ = R2 − , t 2R1 where p is the internal pressure. For this bulkhead a2 > 2b2, so at the edge the hoop stress will be negative, i.e., compressive. In the case of an external pressure being applied, the same expressions are used, but with a negative value for the pressure, which causes compressive stresses as well.

The stresses due to the bulkhead’s own weight (Wb) are [80]

Wb σφ = 2πR t sin2 φ 2 (5.7) Wb σθ = 2 + δR2 cos φ, 2πR1t sin θ where δ is the force per unit volume of the shell.

62 The stresses at the edge resulting from the oxidizer weight can be determined using

γa σφ = (3h + 2b) 6 (5.8) γa σ = (3h(2b2 − a2) − 2ba2 , θ 6b2 and at the bottom using [79] γa2 σ = σ = (h + b), (5.9) φ θ 2b where γ is the propellant specific weight and h is the height of the propellant above the shell.

When the resulting load is compressive, buckling must be considered. According to NASA SP-8032 [76], the stability of an ellipsoidal shell is defined by

 tb 2 2 pcr = 0.14E (5.10) a2 p3(1 − ν2) where pcr is the buckling critical pressure.

Spherical Shell

The theoretical expressions concerning spherical shells will be applied to both ends of both tanks and to the first stage bulkhead. Because these elements are protected by an exterior structure, only their weight, the weight of the fluid being supported and the internal pressure need to be considered as the loading cases. According to [80], the hoop and meridional stresses caused by the internal pressure are the same,

pR σ = σ = . (5.11) φ θ 2t

Due to the spherical shell’s own weight the stresses are [74][80]

W 1 σ = ± · φ 2πRt 1 + cos(φ) (5.12) W  1  σ = ∓ · − cos(φ) , θ 2πRt 1 + cos(φ) where the sign of the expression depends if an upper or a lower dome is being considered. Finally, the stresses caused by the fluid are [80]

γR2  2cos2φ  σ = 2 + φ 6t 1 + cosφ (5.13) γR2  (3 + 2cosφ)2cosφ σ = −2 + , θ 6t 1 + cosφ where γ is defined by

63 W γ = f . (5.14) πd2 (R − d/3)

If the spherical dome is filled, which will always be the case considered, d=R. Wf is the supported fluid’s weight. In the case of the first stage bulkhead, as explained for the second stage one, if the upper part is not pressurized and the lower is, it will support an external pressure, which leads to compressive stresses. This means that a buckling analysis should be made.

According to NASA SP-8032 [76], the classical critical buckling pressure (pCL) for a spherical cap under external pressure is

2  t 2 p = E . (5.15) CL [3(1 − ν2)]1/2 R

The critical buckling pressure is then a function of the classical value,

pcr =λ · pCL

1   2 (5.16) 2 1 R φ λ = [12(1 − ν )] 4 2 sin . t 2

In this case, φ is half the angle included (45o for a dome).

5.3.2 Cylindrical Shells

Although a cylindrical shell is also a shell of revolution, it is often separated from the others, since in this case a straight line, not a curved one, is being rotated around an axis [79]. A shell element is now defined not by two angles, but by the x coordinate and the angle φ, as shown in Figure 5.10. The membrane stresses will therefore be an axial stress σa and the hoop stress σh.

Figure 5.10: Illustration of a cylindrical shell element. Reproduced from [79].

To size the cylindrical elements, the total weight that they support must be determined. The total supported mass is the fairing mass, multiplied by a factor of 1.15 as explained before, plus the payload mass, plus the spherical domes, bulkheads and adapters applicable to each case. The total axial stress due to external axial loading is

64 P σ = a , (5.17) a A where Pa is the axial force and A the projected area.

In addition, the bending moment (Mb) caused by lateral loads (Pl) should also be considered. It is the sum of two components: the mass that the stage supports above itself (mupp) times its length (L) plus the stage’s structural mass (mstr) times the length up to its gravity center (hCG). Both terms are then multiplied by the lateral acceleration (gl), as presented in Equation (5.18). A commonly recommended lateral acceleration for the design process is 2g so this value is used [4][46][81],

Mb = gl (muppL + mstrhCG) . (5.18)

For the cylindrical shell, the second moment of area (I) is equal to πR3t and its projected area (A) to

2πRt. The final expression for the axial stress due to external loads (σa) is

P M R σ = a + b . (5.19) a A I

Along with the external forces, the internal pressure must also be part of this analysis. Considering an uniform internal pressure, the Membrane Theory yields for the axial and hoop stresses [74]

pR σa = 2t (5.20) pR σ = . h t

The buckling analysis, in case it is necessary, can be done using NASA SP-8007. This standard states that for circular cylinders in axial compression buckling coincides with the structural collapse, which makes the buckling stress the dimensioning parameter [75]. It also asserts that the total compres- sive load must be greater than the tensile pressurization load (πpR2) so that buckling can occur and that the destabilizing effects of initial imperfections are reduced by pressurization [75].

The critical buckling stress, in the case of simultaneous axial compression and internal pressuriza- tion, according to this standard, is [75][78]

! Et γ pR σSP 8007 = + ∆γ + cr R p3(1 − ν2) 2t √  − 1 R  (5.21) γ = 1 − 0.901 1 − e 16 t

2 0.75  −3 p R  ∆γ = 0.24 1 − e E ( t ) ,

65 and for an internally pressurized circular cylinder supporting bending stresses,

! Et γ pR σSP 8007 = + ∆γ + 0.8 crb R p3(1 − ν2) 2t √  − 1 R  (5.22) γ = 1 − 0.731 1 − e 16 t

2 0.75  −3 p R  ∆γ = 0.24 1 − e E ( t ) .

Finally, for the combination of the axial and bending loads, the standard proposes a linear relation

σ σ cra/b + cra/b = 1. (5.23) σcra σcrb At this point, the membrane stresses are defined and the structural sizing can be performed, taking into account that the minimum thickness that can be manufactured is considered to be 1 mm. The properties of the materials to be used are summarized in the next section, since their characteristics are needed for the calculations.

5.3.3 Materials’ Properties

As discussed in Section 3.2, the 2024 aluminium alloy will be used for the tanks and a High-Strength carbon fiber composite for the remaining primary structures. Table 5.5 summarizes their properties. The characteristics of the aluminium alloy at cryogenic temperatures were added since these are the ones to take into consideration during the tanks sizing process [22].

Table 5.5: Properties of the selected materials

Parameter Unit Symbol 2024 alloy HS carbon Room Cryogenic

Yield strength MPa σy 355 454 -

Tensile strength MPa σu 483 580 2100 Young’s modulus GPa E 73 85 120 Poisson’s ratio - µ 0.33 - 0.31 Density kg/m3 ρ 2780 2780 1500

5.3.4 Analytical Results

In this section the results obtained with the expressions previously established are presented. Along with the material’s properties, the pressure considered is of 0.5 MPa, as established by Omnidea. When calculating the minimum thickness required, it was concluded that, due to the characteristics of the chosen materials, most components need a thickness inferior to 1 mm to support the loads being applied. A more detailed description of the calculations can be found in AppendixC and the results are summarized in Table 5.6.

66 Table 5.6: Analytical results

Second stage First stage Minimum Design Structural Minimum Design Structural Component thickness thickness mass Component thickness thickness mass [mm] [mm] [kg] [mm] [mm] [kg] Payload fairing 0.02 1 4.7 Interstage 1.5 1.5 19.2 Forward skirt 1.3 1.3 4.3 Upper dome 0.6 1 6.1 Upper dome 0.6 1 6.1 Bulkhead 3.9 3.9 23.7 Bulkhead 3.5 3.5 17.4 Upper cylinder 0.6 1 46.4 Central cylinder 0.6 1 7.9 Lower cylinder 0.6 1 48.4 Lower dome 0.3 1 6.1 Lower dome 0.4 1 6.1 Total 46.5 149.9

During the analytical calculations of the ellipsoidal bulkhead stresses, it was determined that a spher- ical bulkhead is the most beneficial geometry. Although the total stage length needs to be increased, so a spherical dome can fit, mass wise this option is advantageous, since it allows a saving of 44 kg. Since the adapters were sized as well and their mass determined, the margin used for the second stage mass decreases from 1.3 to 1.2 and for the first stage from 1.5 to 1.3. The mass margin for the payload and adapters is kept at 1.15. Including the margins and adding the mass of one engine and of the payload to the second stage’s structural mass, the total dry mass is 140.4 kg, which is 0.4 kg above the estimated. However, if it is established that the lower tank cannot be pressurized before the upper one is, then it is possible to reduce the mass of the bulkhead to the same 6.1 kg as the other domes, as there will be no buckling, thus saving 11.3 kg. This would mean that the stage’s mass would be within the expected value. Regarding the first stage, six engines need to be added, which result in a dry mass of 402 kg, a value below the estimated 580 kg. Additionally, as for the second stage bulkhead, if it is again defined that the lower stage cannot be pressurized when the upper one is not, it is possible to save 17.6 kg. Finally, a numerical analysis was made and its results compared to the analytical ones.

5.4 Numerical Results

For the numerical calculations the software Ansys Structures is used, considering a static structural analysis and the critical load case for each component. Each component is analysed by itself, with the corresponding boundary conditions, since the analytical calculations were done in the same way. The elements used in the mesh were automatically defined by the software. Shell hexahedron ele- ments were mostly used, namely the SHELL181, since the components are thin shell structures. In the case of the spherical domes and the ogive, they were analysed using their mid-surface as reference, so surface elements, specifically the SURF154, were also employed. For the cylindrical components, solid quadrilateral elements, such as SOLID186 were included. Table 5.7 presents the comparison between the analytical and the numerical results.

67 Table 5.7: Comparison of the analytical and numerical results for each structural component

Second stage First stage Analytical Numerical Relative Analytical Numerical Relative Component Stress Component Stress [MPa] [MPa] error [MPa] [MPa] error

σφmax -31.82 -33.63 5.69% Fairing nose Interstage σamax -32.90 -31.65 3.80% σθmax 12.73 11.82 7.15%

σφmax 147.42 147.46 0.03% Forward skirt σφmax -23.00 -22.88 0.52% Upper dome σθmax 147.58 147.64 0.04% σ 147.42 147.46 0.03% σ 99.19 106.60 7.47% Upper dome φmax Upper Cylinder amax σθmax 147.58 147.64 0.04% σθmax 295.00 293.36 0.56% σ -41.13 -41.01 0.29% σ -30.97 -30.88 0.29% Bulkhead φmax Bulkhead φmax σθmax -43.15 -42.38 1.78% σθmax -44.67 -32.11 28.12% σ 122.33 122.25 0.07% σ 90.74 105.89 16.7% Central cylinder amax Lower Cylinder amax σθmax 295.00 294.89 0.04% σθmax 295.00 294.05 0.32% σ 150.83 150.71 0.08% σ 171.52 171.37 0.09% Lower Dome φmax Lower Dome φmax σθmax 152.41 152.07 0.22% σθmax 183.45 172.71 5.85%

The error in the fairing could be due to the Membrane Theory’s available formula for ogives, since it concerns dead loads, which would be its own weight in this case. However, this formula was used to approximate the effects of the drag force as well. The error in the first stage cylinders’ axial stress is also higher than in other cases, because the bending moment caused by the supported mass is not properly considered numerically. A numerical analysis of the entire vehicle would allow a more accurate simulation. It is possible to observe that the higher the supported mass, the higher the bending moment and thus the error. As for the bulkhead and the lower dome, the error is mainly due to the analytical expressions va- lidity. In the analytical method, for a fully filled half sphere, it is considered that the stresses are being calculated at the surface of the fluid, where the formulas are not fully valid. Besides, it is assumed that the entire weight of the fluid is contained in the dome, which is not true since part of the propellant is contained above it. The higher the propellant weight and its free surface above the dome, the higher the error. In AppendixD the preliminary dimensions of the launch vehicle, resulting from this work, are pre- sented.

68 Chapter 6

Conclusion

6.1 Achievements

The main focus of this project was the dimensioning of a launcher’s primary structures. However, the prior bibliographical revision revealed itself a challenging task. Seeing as the space-industry is still pretty restricted, the access to information is often quite difficult, even when concerning past missions. Some of the most reputable references are now out print and prove difficult to find in most libraries. Past that obstacle, trade-off studies were used to compare the various available propellants and materials and to decide which of those best suit this project. After a careful analysis, it was concluded that the combination of liquid oxygen with liquid methane, and a pump-fed system, was the best option. As for the materials, it was determined that the 2024 aluminium alloy is the best option for the cryogenic tanks. However, for structural components not exposed to the propellants, it was the High-Strength carbon fiber composite that presented the best characteristics. The next step was performing an overall aerodynamic sizing. After establishing the atmospheric properties variation with altitude, it was possible to determine the aerodynamic forces. The thrust and gravity force definition was immediate. On the contrary, the drag force depends on many variables and a set of expressions was needed to determine it. The various expressions available were compared so a decision of which to use could be made. After calculating the total drag force, the gravity and drag losses could be computed, so a fineness ratio could be chosen. At this point, it was determined that the initial estimation of the second stage’s dry mass was too optimistic. In addition, when computing the total ∆v needed to reach orbit, it was concluded that more propellant was required to account for this increase in the dry mass. This led to an iterative process, where the first stage was included as well, to determine the total volume of propellants required for the new dry mass inputs. At the end, knowing the new total volume of the vehicle, it was possible to calculate the ideal fineness ratio, i.e., the one that resulted in the lowest drag losses and structural mass. Due to the operational constraints input by the vehicle’s transportation (ship containers), a fineness ratio of 12.7 was determined. The last step before the sizing could be completed was establishing the tanks’ geometry. From the various alternatives, the most advantageous architecture was a central cylinder with

69 spherical caps and a bulkhead. Finally, the dimensioning of the vehicle structural components was concluded through usage of the Membrane Theory for shells. During these calculations, it was verified that a spherical bulkhead for the second stage is more beneficial than an ellipsoidal one, even if it means an increase in the total length, because it results in a lower structural mass. A numerical analysis was also performed, using the Ansys software. After comparing the analytical and numerical results, they mostly seem to be in agreement. In the end, the vehicle’s dimensions result in a lower dry mass than initially estimated. This means that there are two options for the next design iteration. The first is to reduce the propellant quantity, which would result in smaller tanks and could possible lead to the increase of the fineness ratio. This would also lead to lower drag losses, potentially further decreasing the propellants mass needed. The second option would be to keep the same configuration, increasing the payload that the vehicle could carry to the intended orbit. It is concluded that the launcher’s design obtained in this work can be used to accomplish the functional requirements set by Omnidea.

6.2 Future Work

As was previously mentioned, the various subsystems of a launch vehicle are dependent upon each other, and as such this work, a preliminary sizing, cannot be independent from all the other subsystems design. Therefore, the next step is to update the initial mission reference plan provided by Omnidea, using the results here obtained as input. Regarding the parts made from composite materials, the calculations presented throughout this work assumed that the material was isotropic and possessing properties equivalent to those of a High- Strength carbon composite. However, this is a highly idealised scenario, so a more rigorous study should be made about the properties of the material, along with a repetition of the structural analysis of these components. This could possibly allow the decrease of the payload, forward skirt and interstage masses, since the minimum thickness of 1 mm that was considered may not be adequate for this material. As for the structural components, one could also make a more detailed study of the fairing. For instance, the advantages resulting from blunting the nose, as briefly explained in Section 4.2.2, or the possibility of choosing one of the other available geometries should be carefully evaluated. Also, after the engine is fully defined, the thrust frame should be taken into account. Moreover, the propellant management devices, the separation mechanisms and the connections, such as welds or bolts to be used, must be defined. With the connections established, a numerical analysis of the entire vehicle is important to evaluate the load concentration and the interaction between the various parts. Finally, to conclude the design phase, the remaining load sources (as the shocks, operational and transportation loads) must be included for a more thorough analysis and accurate results. Additionally, a modal analysis should be performed to evaluate if the vehicle is able to support the vibrations to which it will be subjected. As the iterative design of the vehicle matures, the safety and project coefficients can be decreased, leading to the final design of the vehicle, which can then be moved to the testing and refinement phase.

70 Bibliography

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79 80 Appendix A

Propellants Reliability

As it was previously mentioned, to evaluate the reliability of the propellants, the failures of all the currently active launch vehicles were studied in order to determine their relation with the propellants or the feed system.

A.1 Launch Vehicles Failures

Most of the failures that happened in the 20th century were due to hardware and software flaws, poor quality control or an insufficient knowledge of how subsystems interact when integrated, amongst other factors. As technology has evolved so substantially in recent years, and engineers have learnt with past mistakes, only failures which have occurred within the last decade have been judged to be relevant. In addition, only the vehicles which have been launched more than 5 times were analysed. Table A.1 represents the launch vehicle reliability statistics as of 2016.

Table A.1: Active launch vehicles that suffered failures in the past 10 years [82]

Launch Vehicle Attempts Successes Reliability Last Failure Soyuz-U 775 754 0.973 2016 Atlas V 68 67 0.985 2016 Proton-M/Breeze-M 89 80 0.899 2014 Tauros XL 9 6 0.667 2011 Safir 8 5 0.625 2012 GSLV 10 5 0.500 2010 CZ-4 (A/B/C) 50 48 0.960 2016 CZ-3 (B/3C) 52 50 0.962 2009 CZ-2 (C)(/SD/SM) 45 43 0.956 2011 CZ-2 (D) 32 31 0.969 2016 Rokot /Briz/K(M) 27 25 0.926 2011 Falcon 9 22 21 0.955 2015

On 2011 a Soyuz-U mission failed when the upper stage experienced a complication owing to a defect in a duct which caused it to block, leading to a cut in the fuel supply and, consequently, the

81 termination of thrust production. [83] Furthermore, in 2016 the upper stage failed again, due to an off-nominal mechanical separation between the third stage and the payload. The liquid oxygen pump caught on fire possibly due to foreign particles present in the pump or to a mistake in the assembly of the engine. It was concluded by the ROSCOSMOS committee that the fire probably led to the opening of the oxidizer tank, leading to further damage to the system. [84] In both cases the engine used a combination of liquid oxygen and kerosene in a pump-fed system. [85] Atlas V had one failure in 2007 and one partial failure in 2016. Jim Sponnick, the ULA (United Launch Alliance, the manufacturer) vice president for Atlas programs, at the time stated that the investigation concluded that the valve lacked enough closing force due to higher than expected friction forces and the very cold temperature of the helium used to operate it. The temperature of the hydrogen also contributed to said friction forces. [86] The propellants used were liquid oxygen and liquid hydrogen with a pump-fed system. [87] In 2016, according to a press release from ULA, an anomaly in the main engine mixture-ratio supply valve caused the first stage to shut down too early. This valve was responsible for controling the ratio of fuel and oxidizer flowing into the combustion chamber and its malfunction led to a reduction in the fuel flow, resulting in engine shut down. This mission was considered a success because the second stage was able to make up for the losses of the first. [88] In this stage, a pump-fed system was also used but with the combination of liquid oxygen and kerosene (RP-1) as propellants. [81] Proton-M/Breeze-M is a configuration of the Proton-M where the upper stage used is the Breeze-M. It has suffered some failures over the past years, namely in 2007, 2008, 2010, 2012, 2013, 2014 and 2015. According to ILS (International Launch Services), who manages the launch services of Proton, in 2007 the failure was owed to a damaged pyro firing cable, which resulted in the failure of separation between the first and second stages. [89] Also, in 2010 the failure was due to an excessive fuel loading [90], in 2012 to a manufacturing defect in a pressurization system component [91] and in 2013 to the improper installation of the yaw sensors [92], so these cases were not related to the propulsion system. In 2008 it was stated that the cause of failure was a ruptured gas duct, which connected the gas generator and the pump turbine, leading to a shut down of Breeze-M’s engine .[93] In addition to the previously mentioned 2012 failure, there was another in December of that same year. It was concluded that this time the cause was a damaged bearing on the oxidizer side of the turbopump, which led to its failure and consequent early engine shutdown of the Breeze-M stage. [94] Moreover, in 2014 it was determined that the loss of structural integrity of a bolted interface in the third stage led to an excessively vibrative environment, which in turn damaged a fuel duct, originating a fuel leak. Because the interface was between the steering engine turbopump and the main engine structural frame, the consequence was loss of stage control and premature shutdown of the engine. [95] The investigators concluded that the reasons for the 2015 failure were the same as the year before. [96]

82 The Breeze-M stage uses a pump-fed system with nitrogen tetroxide as the oxidizer and UDMH as the fuel.[97] Tauros XL suffered two failures: one in 2009 and another in 2011. In both cases the fairing did not separate from the payload so the problem was again not in the propulsion system. [98][99] In addition, it used solid propulsion so it is not useful for a comparison between liquid propellants. [100] Safir is an Iranian launch vehicle and no information was found regarding its failures. GSLV (Geosynchronous Satellite Launch Vehicle) had one failure in 2010, consequence of an anoma- lous stop of the fuel turbopump, likely due to gripping at one of the seal locations or to the rupture of the turbine derived from an excessive pressure rise and thermal stresses. In the end, the supply of liquid hydrogen to the engine was insufficient and so the thrust decayed. [101] This vehicle was propelled by liquid oxygen and liquid hydrogen using a pump-fed system. [102] The CZ or Long March is a family of launch vehicles composed of many different variations and configurations. Regarding variant 4 (CZ-4), the version 4B had a malfunction in 2013 in its 3rd engine. This malfunc- tion was stated to be a result of foreign debris blocking the fuel flow to the engine. It likely originated in the pressurization feeding system or in the assembly process. [103] A pump-fed system was used along with the propellants nitrogen tetroxide and UDMH.[104] In addition, both the configurations 4C and 2D had a failure in 2016, the causes of which are still unknown so these launches will not be taken into account. The version 2C also suffered a failure in 2011, which was said to have been caused by a malfunction of a connection device. [105] When it comes to variant 3 (CZ-3), the vehicle 3B suffered a partial failure in 2009 due to the burn- through of the third stage engine’s gas generator. It was concluded that this was likely caused by foreign matter or icing in the liquid-hydrogen injectors. [106] A combination of liquid oxygen and liquid hydrogen was used in a pump-fed system. Once more, it is known that Rokot suffered an upper stage malfunction in 2011 but the causes are not clear. Falcon 9 suffered its first failure in 2015 when the liquid oxygen tank suffered an overpressure and burst. The cause of this event was a fault in a strut, which caused a breach in the helium system, compromising its integrity. This in turn led to an increase in pressure to a point where the tank could no longer maintain its structural integrity. [107] In 2016 another anomaly occurred when a COPV (composite overwrapped pressure vessel) - used to store the cold helium utilized in the pressurization system - inside the liquid oxygen tank failed. This probably resulted from an accumulation of oxygen between the COPV liner and overwrap, either in a void or a buckle, causing the ignition and consequent failure of the COPV.[31] This was not considered a failure because the vehicle caught fire while still at the launch pad. This vehicle uses liquid oxygen and kerosene in a pump-fed system. [46] Having analysed all the failures that occurred in the past 10 years, Table A.2 was created, in which the number of stage launches using each propellant combination, as well as the number of failures directly related to that combination, were accounted for. Looking at Table A.2, it is possible to see that there is a lack of information about some propellants,

83 Table A.2: Number of stages launched and number of failures related to each propellant combination

Pump-fed system Pressure-fed system

LOX/Kerosene LOX/LH2 N2O4/UDMH N2O4/Aerozine 50 N2O4/MMH N2O4/UDMH

Launches Failures Launches Failures Launches Failures Launches Failures Launches Failures Launches Failures

Soyuz-U [85] 2325 1 Atlas V [81] 68 0 68 1 Proton-M/Brize-M [97] 356 2 GSLV [108][109] 10 1 10 0 CZ-4 [104] 148 1 CZ-3 [110][111] 52 1 52 0 CZ-2 [112][113] 152 0 Falcon 9 [46] 54 1 Delta II [114] 153 0 153 0 Delta IV - M [115] 50 0 Delta IV - H [115] 18 0 Ariane 5 - ECA [4] 118 0 Ariane 5 - ES [116][117] 6 0 6 0 H-IIA [118] 62 0 H-IIB [119] 12 0 PSLV [109][120] 38 0 Dnepr [121] 66 0 Vega [122] 7 0

Total 2600 2 396 3 826 3 153 0 6 0 7 0 because they are not used in currently active vehicles. Also, the number of launches of some vehicles is significantly lower than others, which leads to a deficient comparison of the reliability, as it was shown in Table 3.4 of Section 3.1.1. This issues led to the replacement of the reliability by the TRL, as a parameter used in the propellants trade-study.

84 Appendix B

Structural Mass of Various Tank Geometries

To choose between the various possible tank geometries, it is necessary to evaluate the structural mass of each option. In this appendix the calculations necessary for that analysis are presented, con- sidering the second stage tanks.

The first geometry is presented in Figure B.1.

Figure B.1: Separate tanks configuration.

To determine the dimensions of each component, the total length of 2.8 m will be divided into three parts: the first part (1 m) is where the engine goes so this space cannot be occupied by the tanks, then the bigger tank (oxidizer) will have a maximum length of 0.9 m and the smaller tank (fuel) of 0.85 m. The extra 0.05 m are left empty to allow some free space between the tanks.

Both tanks are then divided in a cylindrical part and two ellipsoidal heads, whose volume (Vell) is given by Equation (B.1). 4 V = πabc (B.1) ell 3

Where a, b and c are the dimensions of the three axis of the ellipsoid. As a=b=R and c will be smaller than R, the ellipsoid is called an oblate spheroid. The surface area (Sell) of this type of geometry is given by Equation (B.2).

85  1 − e2  c2 S = 2πR2 1 + arctanh(e) , e2 = 1 − (B.2) ell e a2

Using each tank volume and maximum length, as it is shown in Equation (B.3), it is possible to determine L and c.

 V = 4 πR2c + πR2L 3 (B.3) L + 2c = Lmax

The dimensions obtained are: Lox = 0.32 m, cox = 0.27 m, Lfuel = 0.31 m and cfuel = 0.22 m. Then, using the aluminium’s density and the minimum thickness of 0.001 m, together with the surface area of both ellipsoids and cylinders, the total mass can be determined. In this case, the oxidizer tank weighs 11.3 kg and the fuel tank 10.8 kg, making a total of 22.1 kg, without considering the adapter needed between the two tanks. Considering the adapter a cylinder with the same thickness, it adds 3.5 kg of mass.

The second configuration is also a central one, but with only one cylinder with spherical tops and divided by a common bulkhead, as shown in Figure B.2.

Figure B.2: Common bulkhead tanks configuration.

The same expressions used for the first case are again used, but this time the main tank dimensions are determined using the total second stage tankage. Then, an additional division in the cylinder and an additional ellipsoidal surface are included. The length of one part of the cylinder will be d and it will determine the ellipsoidal height. Knowing the volume of the corresponding propellant (Vprop), c can be determined.

V − πR2d − 0.5 4 πR3 c = prop 3 (B.4) 4 2 0.5 3 πR

The resulting dimensions are d=0.24 m and c=0.2 m. The total mass in this case is about 22.1 kg.

Finally, the third option consists of two toroidal cylinders, as presented in Figure B.3. In this case, one of the tanks is a larger cylinder, which then contains the second tank, a narrower cylinder, with both having elliptical tops. To determine the cylinder length (Lcyl), the inner radius (Rint) and the elliptical height, c, the following expressions must be solved (considering the fuel tank as the interior one).

86 Figure B.3: Toroidal tanks configuration.

4 V = πR2 c + πR2 L (B.5) fuel 3 int 1 int cyl 2 2 Vox = πR Lcyl − πRintLcyl + Vtorus (B.6) R − R  R − R  V = 2π2c int int − R (B.7) torus 2 2 2 int

This results in a length of 1.2 m and an inner radius of 0.4 m. Using once more the surface areas of both cylinders and resorting to the online tool Wolphram Alpha to determine the elliptic torus surface area, the total mass is 31 kg.

87 88 Appendix C

Analytical Sizing

C.1 Second Stage

The second stage is composed of the payload fairing, a forward skirt and the propellant tanks. Fig- ure C.1 presents these structural elements.

Figure C.1: Structural components of the second stage.

Fairing

For the fairing, at the edge, the resulting maximum meridional stress at lift-off is -78.6 kPa and the maximum hoop stress is 31.5 kPa. The hoop stress has a maximum compressive value of -13.7 kPa around φ = 51o. When the drag reaches its maximum value, the meridional stress at the edge is -31.8 MPa, the hoop stress is 12.7 MPa and the maximum compressive stress is -5.5 MPa. If there was no thickness limitation, a thickness of 2 × 10−5 mm would be sufficient to support these loads. The resulting mass of the ogive is about 4.7 kg. A numerical buckling study is needed to evaluate if buckling will occur, since no analytical expression was found. Doing a linear buckling analysis using again the Ansys software, the expected buckling load is -127 kN which is higher than the design load of -51.4 kN so no buckling is expected.

89 Forward skirt

A small adapter must exist between the tanks and the fairing. This is called a forward skirt and its height will be equal to the radius of the upper spherical dome. Since this part won’t be pressurized, the critical sizing case is when the compressive force is maximum. Considering the adapter as a cylinder supporting the fairing, a minimum thickness of 1×10−5 mm would be needed. Considering the minimum value of 1 mm, the maximum axial stress is -29.9 MPa. Using Equations (5.21) to (5.23), the buckling stress is -22 MPa, so buckling will occur. To prevent it, a thickness of 1.3 mm is required, resulting in a maximum axial stress of -23 MPa and a critical buckling stress of -31 MPa. This part will add 4.3 kg to the structural mass of the stage.

Upper spherical dome

Considering the lift-off phase, the shell’s apparent weight will be the only external loading source. In this case, a thickness of 6×10−4 mm would be enough. For a thickness of 1 mm, the resulting maximum stresses at the edge are 147.4 MPa and 147.6 MPa, in the meridional and hoop directions, respectively. At the top the stresses are of 147.5 MPa. Since this part will not support the drag force, the stresses at the point of maximum drag are the same. This component will have a mass of 6.1 kg.

Bulkhead

From the three loading cases that the bulkhead supports, the one where an external pressure is applied leads to the higher stresses and so it is the critical dimensioning case. Due to the external pressure there will be a compressive axial stress applied at the edge. However, it is the tensile hoop stress that defines the thickness required to support the loads: 2.2 mm. With this, according to NASA SP-8032, the bulkhead is expected to be unstable. A minimum thickness of 18 mm is required. The resulting meridional and hoop stresses at the edge are -8.1 MPa and 54.4 MPa, respectively. At the bottom the meridional stress is -23.9 MPa and the hoop stress is -24 MPa. The final mass is 66.4 kg. After this analysis it is concluded that due to the small ratio between the major and minor axis, the bulkhead will be thicker, and consequently heavier, compared to the other elements already sized. In the limit, the ellipsoidal bulkhead could be changed to a spherical one (ratio of 1), increasing the length of the tank by 15 cm. Repeating the analysis for a spherical bulkhead, for the case of external pressure, according to Equation (5.16) a thickness of 1 mm would result in buckling. The minimum thickness to avoid buckling is of 3.5 mm, which results in a critical stress of -44.1 MPa and in the maximum stresses of -41 MPa (meridional) and -43 MPa (hoop). As it was previously explained, either at lift-off or at the point of maximum drag, the bulkhead will be pressurized both internally and externally so the stresses due to the pressure are null. With a thickness of 3.5 mm the stresses due to the bulkhead’s and oxygen’s weight are below the maximum stresses determined before (about 4 MPa), so the sizing of this component is finished.

90 In conclusion, the spherical bulkhead’s mass is 21.3 kg, which allows a saving of 44 kg (considering the increase in the cylinders length) when compared to the ellipsoidal bulkhead, so this was chosen as the final configuration.

Cylinder

In the case of the cylinder, the minimum thickness required is 6×10−4 mm. Using the minimum value, the resulting stresses are 145.9 MPa (axial) and 295 MPa (hoop) at lift-off. When the maximum drag is reached, the axial stress decreases to 121.8 MPa due to the higher compressive force that counteracts the internal pressurization. As the resulting stresses are tensile ones, the buckling analysis is not necessary. The component will weigh 7.94 kg.

Lower spherical dome

Knowing that this dome will support the liquid methane, which has a density of 423 kg/m3, a thickness of 3.4 × 10−4 mm is necessary to support the loads. For a thickness of 1 mm, at lift-off the maximum stress is 152.2 MPa, at the bottom of the dome. When the drag force is maximum, as the acceleration will be higher, the stresses due to the fluid will also be higher, and so the maximum stress increases slightly to 152.4 MPa. This dome will have the same mass as the upper one (6.1 kg), since the thickness is the same.

C.2 First Stage

Regarding the first stage, along with the propellant tanks, it includes the interstage, as shown in Figure C.2.

Figure C.2: Structural components of the first stage.

91 Interstage

The interstage, which is the structural element that connects the first and the second stages, is an unpressurised cylinder, which will support the weight of the upper stage. For a thickness of 1 mm, according to NASA SP-8007 (Equations (5.21) to (5.23)) buckling would occur. To avoid buckling a thickness of 1.5 mm is need, which results in a maximum compressive axial stress of 33 MPa and a critical buckling stress of 38 MPa. The interstage will therefore weigh 19.2 kg.

Upper spherical dome

The upper dome of this stage is under the same conditions as the upper dome of the second stage, so the previous results are valid for this case as well.

Bulkhead

When considering the first stage’s bulkhead, the dimensioning case will again be when the lower part is pressurized and the upper is not, causing a compressive pressure differential. Considering that at the same time it supports its own weight and the entire volume of liquid oxygen (4.94 m3), it requires a minimum thickness of 0.3 mm. However, in order to avoid buckling, the thickness has to be increased to 3.9 mm. The resulting maximum meridional stress is -31 MPa, the maximum hoop stress is -45 MPa and the critical stress is -49 MPa. The mass of this element is 23.7 kg.

Cylinder

As for the central cylinder, it will be divided into two parts: upper cylinder, above the bulkhead, and lower cylinder, below the bulkhead. The upper cylinder will support the weight of the second stage, the interstage and its upper dome. A thickness of 0.6 mm was needed to support the loads. For the minimum thickness, the maximum axial stress at lift-off is 123.9 MPa and when the drag is maximum it decreases to 99.2 MPa. As the hoop stress only depends on the radius, pressure and thickness, it is the same as for the second stage’s cylinder. The upper cylinder has a mass of 46.38 kg. Regarding the lower cylinder, that will additionally support the bulkhead and the upper cylinder, the axial stress is 115.5 MPa at lift-off and 90.7 MPa at maximum drag. This lower part has a mass of 48.44 kg.

Lower spherical dome

Finally, the lower dome supports its weight, the internal pressure and the weight of the liquid methane. At lift-off the volume will be at its maximum (4.43 m3) but when drag is maximum, part of this volume has been spent and only about 4 m3 remain, so the applied stress will be lower. Again, a thickness of 0.4 mm would suffice to support the loads. Using 1 mm, at lift-off the maximum stress is 183.5 MPa and at the point where the drag is maximum, the maximum stress is 181.5 MPa.

92 Appendix D

Launch Vehicle Layout

93 1

1200 2 A 3 1 590 1 B 4 770 5 1 3.5 6

2300 7 DETAIL A DETAIL B C 8

1.5 1 1 3.9 9

4500 1 14050 DETAIL C DETAIL D D 10

Reference Name Material Number 1 Fairing HS Carbon 11 2 Forward Skirt HS Carbon

4700 3 Second Stage Upper Dome AL 2024 4 Second Stage Bulkhead AL 2024 5 Second Stage Central Cylinder AL 2024 6 Second Stage Lower Dome AL 2024 7 Interstage HS Carbon 8 First Stage Upper Dome AL 2024 12 9 First Stage Upper Cylinder AL 2024

590 10 First Stage Bulkhead AL 2024 11 First Stage Lower Cylinder AL 2024 12 First Stage Lower Dome AL 2024 1180