Design and construction of a vertical landing vehicle using a cold gas thruster

BACHELOR FINAL THESIS Design and Construction of a Vertical Landing Vehicle using a Cold Gas Thruster Author: Sylvain L. Walsh Director /Co-director: Jaume Solé Bosquet Degree: Bachelor in Aerospace Vehicle Engineering Examination session: Spring, 2021 Document: Report ESEIAAT Final Bachelor Thesis Escola Superior d’Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa Universitat Politècnica de Catalunya Bachelor in Aerospace Vehicle Engineering Design and Construction of a Vertical Landing Vehicle using a Cold Gas Thruster REPORT Author: Sylvain L. Walsh Director: Jaume Solé Bosquet June 22, 2021 Disclaimer I Sylvain Walsh, certify that this report is my own work and that all sources of information used in this report have been fully acknowledged. Copyright cbna 2021. This work is licensed under a CC BY-NC-SA 4.0 license. To view a human-readable summary of the license visit: https://creativecommons.org/licenses/by-nc-sa/4.0/ Abstract Universitat Politècnica de Catalunya Escola Superior d’Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa Design and Construction of a Vertical Landing Vehicle using a Cold Gas Thruster Sylvain L. Walsh With the “New Space” era we are now seeing a prominent rise in the development of Reusable Launch Vehicles with vertical landing capabilities. This project aims to design and construct a scaled model of such a vehicle but using a cold gas thruster as a means of propulsion. In order to do so, multiple disciplines of engineering are required to develop critical systems such as retro-propulsion, thrust vector control and aerobraking. From structural simulations and CFD analysis to stabilization algorithms and FDM manufacturing, all the methods employed to carry out this complex task presented their complications and challenges, all of which had to be recorded, analysed and overcome. The propellant chosen for the task of propulsion was compressed air, due to its compatibility and availability. Design requirements were established from the beginning but as the project evolved it was clear several of these could not be realized due to limitations of the components available. Most noticeably, the maximum thrust value was found to be restricted by the propulsion system, which makes it impossible to achieve sufficient deceleration for a controlled landing. Having said that, the project successfully lays down the foundations for future iterations and outlines the next steps required in order to solve the main issues related to thrust. If these issues were to be resolved, there is confidence in coming closer to the project’s aim of using compressed air as a means of propulsion. Resum Amb l’era del "New Space" estem veient un augment destacat en el desenvolupament de "Reusable Launch Vehicles" amb capacitat d’aterratge vertical. Aquest projecte té com a objectiu dissenyar i construir un model a escala d’un vehicle de l’estil però que utilitza un propulsor de gas fred com a mitjà de propulsió. Per fer-ho, es requereixen múltiples disciplines d’enginyeria per desenvolupar sistemes crítics com ara la retropropulsió, el control d’empenta i l’aerofrenament. Des de simulacions estructurals i anàlisi de CFD a algorismes d’estabilització i fabricació de FDM, tots els mètodes empleats per dur a terme aquesta complexa tasca han presentat les seves complicacions i desafiaments que s’han hagut analitzar i superar. El propulsor triat per a la tasca és l’aire comprimit, per la seva compatibilitat i disponibilitat. Diversos requisits de disseny s’han establert des del principi, però a mesura que el projecte ha anat evolucionant, ha quedat clar que n’hi ha uns que no s’ha pogut realitzar a causa de les limitacions dels components disponibles. El més notable és la constricció de la màxima empenta a causa del disseny del sistema propulsor, cosa que ha fet impossible aconseguir suficient desacceleració per a un aterratge controlat. Dit això, el projecte estableix amb èxit les bases per a futures iteracions i els passos següents per a prendre s’identifiquen clarament per resoldre els principals problemes relacionats amb l’empenta. Si aquestes qüestions es resolguessin, hi ha confiança en apropar-se a l’objectiu del projecte mitjançant l’aire com a propulsor. Acknowledgements This project couldn’t have been completed without the continued support of my parents, not only did they finance the project, but they have always been available to give a helping hand or to deliver observations or insight not innate to me. I would also like to give a sincere thanks to Jaume Solé Bosquet, my project director, for his constant guidance as well as for providing much necessary information and helping me to make decisions that guided the project in a better direction. These acknowledgements wouldn’t be complete if I didn’t mention my extended family, friends and colleagues, who have always believed I was capable of managing such a complex task and for motivating me to carry on even when the odds were stacked against me. Finally I’d like to thank my high school, Súnion, for letting me use their installations for carrying out the drop tests necessary for the development of this project. Contents Abstract iii Acknowledgements v Contents vi List of Figures viii List of Tables x Notation xii Glossary xiv 1 Introduction 1 1.1 Aim ........................................ 1 1.2 Scope ....................................... 1 1.2.1 High Level Deliverables . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Requirements................................... 3 1.4 Background.................................... 3 1.5 Justification.................................... 4 2 Development 5 2.1 StateoftheArt.................................. 5 2.1.1 Basic Mechanics of a Falling Body . . . . . . . . . . . . . . . . . . . 5 2.1.1.1 Stability ............................ 6 2.1.2 Vertical Landing Reusable Launch Vehicle . . . . . . . . . . . . . . . 6 2.1.3 ColdGasThruster............................ 8 2.2 Identification and Selection of Options . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Propellant Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Active Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2.1 Thrust Vector Control . . . . . . . . . . . . . . . . . . . . . 13 2.2.2.2 Adjustable Fins . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.2.3 Reactive Control System . . . . . . . . . . . . . . . . . . . 15 2.2.3 Additional Decision Making . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 InitialParameters ................................ 17 2.3.1 FlightProfile ............................... 17 2.3.2 Required Thrust Algorithm . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.2.1 Algorithm Flowchart and Results . . . . . . . . . . . . . . 18 2.3.3 BurnAlgorithm ............................. 24 2.3.3.1 Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.3.2 Thermodynamic Equations . . . . . . . . . . . . . . . . . . 26 2.3.3.3 Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.3.4 Algorithm Flowchart and Results . . . . . . . . . . . . . . 27 3 Design and Construction 32 3.1 PropulsionSystem ................................ 32 3.1.1 ThrustTestBench............................ 35 3.1.2 Nozzles, Tests and Troubleshooting . . . . . . . . . . . . . . . . . . . 36 3.1.3 TheCoandaNozzle ........................... 44 3.1.4 FinalNozzleDesign ........................... 46 3.2 ThrustVectorControl.............................. 48 3.3 Aerobrakes .................................... 50 3.3.1 CFDSimulation ............................. 51 3.3.2 Aerobrake Mount Design . . . . . . . . . . . . . . . . . . . . . . . . 54 3.4 Retractable Landing Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.4.1 Structural Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.5 Electroniccircuit................................. 61 3.5.1 QuickRelease............................... 63 3.6 Structure ..................................... 66 3.6.1 Topology Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.6.2 FDMParameters............................. 67 3.6.3 Mass and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4 Software Development 70 4.1 PIDController .................................. 70 4.2 Closed Loop System Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3 PIDTuning.................................... 73 4.4 Program...................................... 77 4.4.1 LaunchSequence............................. 77 4.4.2 Characteristics and Functions . . . . . . . . . . . . . . . . . . . . . . 78 4.4.2.1 𝐼2𝐶Communication Protocol . . . . . . . . . . . . . . . . . 78 4.4.2.2 LiDAR Correction . . . . . . . . . . . . . . . . . . . . . . . 78 4.4.2.3 PID Implementation . . . . . . . . . . . . . . . . . . . . . . 78 4.4.2.4 Servo Position Parametrization . . . . . . . . . . . . . . . . 79 4.4.2.5 Program Flowchart . . . . . . . . . . . . . . . . . . . . . . 79 4.4.3 CodeOptimization............................ 81 5 Validation and Results 82 5.1 DummyDropTest ................................ 82 5.2 Static Stabilization Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.3 NextSteps .................................... 86 6 Budget 88 7 Environmental Aspects 89 7.1 Energy Consumption Impact . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.2 Materials ..................................... 89 8 Conclusions 90 References 92 List of Figures 2.1 Terminalvelocitydiagram .............................. 5 2.2 Vertical landing vehicle stabilization . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Retro-propulsion schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Falcon 9 booster stage landing on ASDS [5] .................... 7 2.5 Thrust Vector Control schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 cold gas thruster schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.7 Carbon dioxide pressure-temperature phase diagram [9].............. 11 2.8 Thrust Vector Control alternatives [11]....................... 14 2.9 Reaction Control System schematic . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.10 Render of initial aerobrake model . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.11 CFD analysis of initial aerobrake model . . . . . . . . . . . . . . . . . . . . . . 17 2.12 CFD analysis of initial vehicle body model . . . . . . . . . . . . . . . . . . . . . 18 2.13 Required thrust Matlab algorithm flowchart . . . . . . . . . . . . . . . . . . . . 19 2.14 Required thrust algorithm results for a drop height of 20m . . . . . . . . . . . . 20 2.15 Required thrust algorithm results for a drop height of 40m . . . . . . . . . . . . 21 2.16 Required thrust as a function of vehicle mass . . . . . . . . . . . . . . . . . . . 22 2.17 Required thrust as a function of non-dimensional igntion height . . . . . . . . . 23 2.18 Lambda nozzle correction factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.19 Joule-Thomson inversion curves [16]......................... 26 2.20 Flowchart of the Burn algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.21 Burn algorithm results of tank density, pressure and thruster specific impulse . 29 2.22 Burn algorithm results of mass flow rate, flow factor and propellant mass . . . . 30 3.1 Constructed pneumatic propulsion system and its components . . . . . . . . . . 33 3.2 Pneumatic propulsion system diagram . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Thrust test bench CAD render . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4 Thrusttestbenchsetup ............................... 35 3.5 Render of first nozzle iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.6 Initial nozzle dimensions and geometry . . . . . . . . . . . . . . . . . . . . . . . 37 3.7 Initial nozzle thrust curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1: A cold gas thruster is a type of rocket thruster that produces thrust using the expansion of a pressurized gas. Usually the gas used is inert. 2: Mathematical method that optimizes material layout within a defined mesh for a given set of loads, boundary conditions and constraints. Introduction 1 1.1Aim ................ 1 1.2Scope............... 1 1.3 Requirements . . . . . . . . . 3 1.4 Background . . . . . . . . . . 3 1.5 Justification . . . . . . . . . . 4 This section introduces the project by setting out it’s aim, the scope that specifies what elements have been carried out, the requirements to be met, a justification explaining the necessity that the project covers and finally a brief background study including current information and a review surrounding the area being researched. 1.1 Aim The aim of the project is to design and construct a scaled prototype of a reusable Vertical Landing Vehicle (VLV) with retro-propulsive and flight stabilization capabilities. To be more specific, thrust will be achieved by means of a cold gas thruster.1 1.2 Scope In order to attain this aim, many aspects needed to be realized. The most important of which are the following: I The design and implementation of a pneumatic system in charge of providing thrust in order to decelerate the vehicle. IAcquirement of active stabilization by means of TVC. I Implementation of aerobraking using deployable fins in order to stabilize the vehicle and further decelerate it. A CFD study of the aerobrakes and rocket body will be carried out in order to assess performance. I Development of algorithms in Matlab to determine flight profile and preliminary design parameters. IConstruction of a thrust test bench using a Wheatstone Bridge IInvestigation of experimental coanda nozzle technology. I Design and construction of deployable landing legs making use of Solidworks structural impact simulations. I 3D cad design of 30+ components using Solidworks , all of which manufactured using FDM. I Implementation of topology optimization2 with the objective of reducing component weight. 1 Introduction 2 I Design of an electrical circuit with all the components necessary for operation. I Simulation of the flight dynamics and closed loop control system in Simulink and implementation of a PD controller to stabilize the vehicle. IDevelopment of code to control the Arduino flight computer I Validation of aerobrake and leg design by means of a dummy test flight consisting in dropping the full mass vehicle from a height of 15m. I Validation of the closed loop stabilization algorithm using static flight tests. The scope of the project excludes: I Economic feasibility analysis: The project is of scientific purpose and therefore is not intended to be commercialized. I The vehicle is only meant to perform vertical landing. Consequently, powered launching options and capabilities will not be considered nor implemented. Flight will be achieved by dropping the vehicle from a predetermined height. IA live telemetry transmission and receiving system. 1.2.1 High Level Deliverables IA. Constructed vehicle: Completed construction of vertical landing vehicle IB. Vehicle technical sheet: Technical sheet including thrust, mass breakdown, list of components and materials, MMOI , performance parameters. IC. Drawings: Drawings of CAD designed parts and assemblies. ID. Circuit schematic: Electronics schematic detailing all the components used and the connections made. IE. Budget: Breakdown of component, material and person-hours costs. IF. Propulsion system diagram: Pneumatic diagram of the propulsion system containing the components that form it. 1 Introduction 3 1.3 Requirements The following requirements were set at an early stage of the project and were chosen in order to accomplish the project’s goal. IREQ-001 : Vehicle shall be capable of decelerating using a cold gas thruster as a means of retro-propulsion. IREQ-002 : Vehicle shall be capable of active stabilization with the use of Thrust Vector Control. IREQ-003 : Vehicle shall be capable of sustaining hovering flight. IREQ-004 : Vehicle shall be capable of complete autonomous flight. IREQ-005: Vehicle shall be reusable. IREQ-006: Vehicle shall have a lightweight design. IREQ-007 : Vehicle shall have FDM manufactured parts for educational purposes. 1.4 Background As far as space history goes, we are currently living the New Space era. "New Space" refers to the commercialization of the space sector. The movement is impulsed on the basis that space is one of today’s major growth industries. The space telecommunications sector generates revenue of over €100 billion each year[1] [1]: Airbus (2021), New Space - Space - Airbus . Some of the better well known companies that are driving the movement include SpaceX, Virgin Galactic and Blue Origin. These companies all have one thing in common: they are engineering and constructing RLVs, a lot of which are capable of vertical retro-propulsive landing. The reason behind this technology and the goal that it’s seeking to achieve, is the reduction in launch costs with the use of the re-usability aspect that these vehicles possess. So, has this goal been achieved? NASA ’s Space Shuttle had a cost of around $1.5 billion to launch 27,500kg to LEO, whilst SpaceX’s Falcon 9 now advertises a launch cost of $62 million to bring 22,800kg to LEO. This works out to 54,500$/kg and 2,720$/kg accordingly, a reduction of a factor of 20 [2] [2]: Jones (2018), ‘The Recent Large Reduction in Space Launch Cost’ . A common misconception is that this impressive reduction in launch costs is due solely to the reusability aspect, but as of today, the main reason behind the reduction is the deinstitutionalization of spaceflight and development. Contrarily to government subsidized institutions such as NASA or ESA , commercial spaceflight companies have the luxury of developing in a unconstrained environment and therefore can provide drastically cheaper launch costs. Back in 2010, NASA used it’s Air Force cost Model (NAFCOM) [3] [3]: NASA (2011), Falcon 9 Launch Vehicle NAFCOM Cost Estimates in order to obtain an estimation of how much it 1 Introduction 4 3: Vertical landing with solid motors has been achieved with many iterations, exact flight telemetry and perfect ignition timing. The problem of this approach is the difficulty in obtaining repeatably since every solid rocket motor burns differently and produces different thrust curves due to chemical and fabrication imperfections. For more information on solid motor vertical landings check out Joe Barnard’s website. He runs the BPS Space YouTube channel which has provided the author with knowledge on some of the concepts involved with vertical landing. 4: Solid rocket motors burn highly flammable propellants and if not used correctly can cause serious injury or death. would of cost them to develop the Falcon 9. The results were clear: It would have cost NASA $1.14 billion using traditional institutionalized contracting, whilst the total cost for SpaceX was $443 million, a 63% reduction. The point is that as of today the reduction in launch costs is not on account of the reusability aspect, but rather the deinstitutionalization factor. The reusability aspect still hasn’t gained relevance due to the fact of the high developments costs that RLV vehicles involve. Having said that, like space industry analyst Ajay Kothary puts it, SpaceX’s reusable technology could do for space transport ‘what jet engines did for air transportation sixty years ago when people never imagined that more than 500 million passengers would travel by airplanes every year and that the cost could be reduced to the level it is—all because of passenger volume and reliable reusability’. [4] [4]: Kothary (2014), The Space Review: Robust and reusable? In time, when the development costs of said vehicles and the tweaking of operations are likely to bring to evidence the potential of RLV. In January 2014 SpaceX said that if they were successful in delivering reusable technology, launch prices of as low as from $US5 to 7 million were possible. Following the first successful retrieval of a Falcon 9 first stage, back in 2015, Elon Musk stated that ‘the potential cost reduction over the long term is probably in excess of a factor of 100’ 1.5 Justification The main necessity that this project aims to cover is the deepening of knowledge on the broad range of disciplines and technologies required for the engineering and construction of a vertical landing Reusable Launch Vehicle (RLV) , a vehicle that, as exposed in the previous section, is likely to lead the space industry in the near future. Another need the project addresses is the integration of cold gas thruster technology into the model rocketry world. This field has developed an interest in designing vehicles with vertical landing capabilities following the footsteps of the New Space movement, but it has one major design constraint: solid fuel motors. The nature of these motors makes throttling them almost impossible and once they are ignited, they burn until exhausting all of the propellant. This is a major setback when attempting vertical retro-propulsive landing where throttling is essential. 3 Using a cold gas thruster controlled with a solenoid valve allows for the thrust to be throttleable and controlled in a closed loop control system, making the objective easier and safer 4 to accomplish. The proposed technology will not have enough thrust to launch model rockets, but if it works, it could be integrated to the upper stages of rocket designs allowing for vertical landings, safely returning to ground any payload within. 1: The drag coefficient is a dimensionless quantity that is used to quantify the drag of a body in a fluid environment. Drag coefficients are always associated to a specific reference area. Figure 2.1: Representation of gravitational force and drag force. The net force is 0 and therefore the body does not accelerate. Own elaboration. Development 2 2.1 State of the Art . . . . . . . 5 2.2 Identification and Selection of Options . . . . . . . . . . . . 10 2.3 Initial Parameters . . . . 17 2.1 State of the Art In this section a brief analysis of multiple concepts will be carried out in order to properly understand the playing field and what is to be expected as the project progresses. At first focusing on the flight mechanics of vertical landing, then analysing the Falcon 9 booster stage and finally concentrating on the essential subsystems specific to this project. 2.1.1 Basic Mechanics of a Falling Body When dropping an initially stationary body with mass, it will enter a free fall accelerating towards the centre of the earth at a rate of 𝑔= 9 . 81 𝑚 𝑠2 . This behaviour can described with Newton’s law of universal gravitation, which if applied for relatively short vertical distances, can be simplified like so: 𝐹=𝑚·𝑎(2.1) where in this case 𝑎=𝑔; If there was no atmosphere present, the body would accelerate indefinitely, but this is not the case. Earth has an atmosphere that creates drag on any body in motion due to the interaction between the body’s surface and the fluid (air) that surrounds it. The drag that is generated is always oriented opposite to the direction of travel of the object and can be expressed as: 𝐷=1 2·𝜌·𝑉2·𝐴·𝐶𝐷(2.2) where 𝜌is air density, 𝑉is velocity, 𝐴is reference area and 𝐶𝐷is the body’s drag coefficient.1 Therefore, in a fluid environment such as the earth’s atmosphere, a body will gain velocity and therefore drag, until drag and gravitational force equal out. When this occurs the body no longer accelerates and falls at a constant velocity. This velocity is known as terminal velocity. Furthermore, it is known that a body that isn’t not fixed, for instance a body in free fall, will rotate about it’s center of mass COM. Additionally, any forces that act on the body and are not aligned wit the COM, will generate torque that will induce rotation. The body’s resistance to this torque is known as the MMOI. 2 Development 6 2.1.1.1 Stability Another important aspect to have in mind is stability. To understand if a body in a fluid will behave in a stable or unstable way it’s essential to know the position of the body’s center of pressure. The center of pressure is the point where the total sum of the pressure field acts on the body. In other words, it’s the point where aerodynamic (drag and lift) forces are applied. When a vertical landing vehicle tilts with respect to it’s velocity vector, it will generate lift which induces torque about the COM. This torque can be stabilizing or restoring. Figure 2.2: The vehicle on the left produces destabilizing torque while the vehicle on the right produces restoring torque. Own elaboration The difference between the two vehicles in Figure 2.2 is the position of the CP relative to the COM. The conclusion drawn is that for a vertical landing vehicle to be stable, the COM must be positioned below the CP (adhering the orange coordinate system in Figure 2.2). Design Requirement 2.1 In order for the vehicle to be stable, the center of mass must be situated below the center of pressure. 2.1.2 Vertical Landing Reusable Launch Vehicle A vertical landing RLV is a vehicle capable of launching with its own thrust, sustaining flight and a specific trajectory for a certain amount of time and finally returning safely to the ground whilst performing vertical landing. As an example, SpaceX’s Falcon 9 booster stage will be analyzed. This booster is able to perform all operations mentioned above and, even though this project does not deal with the launching aspects, it’s analysis will serve for fully understanding what systems 2 Development 7 Figure 2.4: Retro-propulsion points the thrust opposite to the direction of travel. In this case the net force is not 0 and therefore the vehicle decelerates. Own elaboration and processes are necessary to perform vertical landing. Figure 2.3: Falcon 9 booster stage instances before touchdown on the Autonomous Spaceport Drone Ship. "First stage of Falcon 9 rocket" by Official SpaceX Photos is licensed under CC BY-NC 2.0 [5] First of all and most noticeably, the Falcon 9 possess a propulsion system powered by 9 Merlin engines that, during reentry and landing, points the thrust vector opposite to the direction of travel. This condition is known as retro-propulsion and serves to decelerate the vehicle from terminal velocity to standstill at touchdown; as shown in Figure 2.3 and schematically in Figure 2.4. When it comes to active stabilization the Falcon 9 booster has 2 methods of keeping the rocket vertical during reentry and landing: TVC and adjustable fins. Thrust Vector Control is a commonly used technique with aerospace vehicles. Broken down to the basics, it consists on offsetting the thrust vector in such away that it miss-aligns with the COM and as a result a net torque. This torque is then used to tilt and effectively stabilize the vehicle. There are many ways for bringing this technique about and they will be detailed in Section 2.2. Figure 2.5: Thrust Vector Control schematic. The lateral thrust component Tx creates torque about the vehicle’s COM The second method for stabilization is the use of adjustable rotating 2 Development 8 grid fins. When the fins rotate about their axis they deflect the airflow passing through them, resulting in lift that produces torque. In order to control the retro-propulsion and torque, the Falcon 9 booster possesses avionics which include flight computers, GPS , IMUs2 2: An Inertial Measuring Unit is an electronic device composed of multiple sensors that capture data on the movement of a body. Typically the sensors that are found in an IMU are: I Accelerometers that measure velocity and acceleration I Gyroscopes that measure rotation and rotational rate I Magnetometers that are capable of determining directional heading and controllers [6] [6]: Space Exploration Technologies Corp (2020), Falcon User’s Guide . The data recorded by the vehicle’s sensors is fed into a closed loop control system which uses the feedback to command the control systems mentioned above. More information on closed loop controllers can be found in Section 4.1. The final aspect of the booster worth analyzing when it comes to vertical landing is, quite intuitively, the landing legs. These legs must be retractable in order to minimize drag and disturbances during launch and flight. Design Requirement 2.2 Landing legs must be retractable. To sum up, in order to successfully achieve a vertical landing the following systems are required: IRetro-propulsion system IActive stabilization by means of TVC and fins IFlight computers and avionics IRetractable landing legs Having taken a look at the general systems involved in a real life vertical landing RLV, it’s now necessary to consider the concepts specific to this project. 2.1.3 Cold Gas Thruster The aim of the project is to obtain retro-propulsion employing a gold gas thruster. A cold gas thruster is a propulsion system that creates thrust by expanding a highly compressed gas. The gas used for the propulsion is typically inert. The thruster is composed of two main elements: the propellant storage that stores the pressurized gas and a nozzle that expands the compressed gasses in order to produce thrust. Figure 2.6: Simplified schematic of forces involved in a cold gas thruster. P3 is ambient pressure, P2 is the tank pressure, the yellow vectors represent the tangential forces generated as a consequence of the gas’s viscosity, and in red the velocity vector of the expanded gases at the nozzle exit section. The smallest section of the nozzle is the throat. Note that all forces are surface forces.Own elaboration. 2 Development 9 3: Symbolized as Δ𝑉 , delta-v is a measure of impulse per unit of time required to perform a maneuver. The thrust produced by a cold gas thruster is obtained from to the sum of external forces and internal forces [7] [7]: Sutton et al. (2001), Rocket Propulsion Elements Seventh Edition and is equal to: 𝑇=¤ 𝑚𝑢2+ (𝑃2−𝑃3)𝐴2(2.3) where ¤ 𝑚 is the mass flow rate, 𝑢2 the escape gas velocity, 𝑃2 the gas pressure at the exit, 𝑃3 the ambient pressure and 𝐴2 the cross section area of the exit. It’s important to note that the cold gas thruster does not house combustion. This basically means that it produces lower thrust and less efficiency than conventional monopropellant or bipropellant rocket engines. In order to compare efficiencies specific impulse or 𝐼𝑠𝑝 is used: 𝐼𝑠𝑝 =𝑢2 𝑔0 (2.4) where 𝑢2 is the exhaust velocity and 𝑔0 is standard gravity. It’s units are seconds [s]. 𝐼𝑠𝑝 measures how efficiently a propulsion system creates thrust. A system with higher 𝐼𝑠𝑝 uses the mass of the propellant more efficiently, and in the case of a rocket this means less propellant is needed for a certain amount of delta-v 3 . In other words, the higher the 𝐼𝑠𝑝 , the less propellant mass is needed and therefore the vehicle’s wet mass reduces, requiring less thrust to slow down. Design Requirement 2.3 Obtain the highest 𝐼𝑠𝑝 as possible in order to reduce the vehicle’s wet mass and consequently reducing the required thrust. As can be seen in the following equation, specific impulse is affected by the thermodynamic state of the propellant and the nozzle geometry: 𝐼𝑠𝑝 =1 𝑔v u t2𝛾 𝛾−1·𝑅𝑠𝑝 ·𝑇𝑐"1−𝑃𝑒 𝑃𝑐𝛾−1 𝛾#(2.5) where 𝑅𝑠𝑝 is the specific gas constant ( 𝑅/𝑀 ), 𝛾 the propellant heat capacity ratio, 𝑇𝑐 is the combustion chamber temperature and 𝑃𝑒 𝑃𝑐 the external-chamber pressure ratio, characteristic to the nozzle geometry. Immediately one can see that the components that favour 𝐼𝑠𝑝 are 𝑅𝑠𝑝 and 𝑇𝑐 . Since cold gas thrusters don’t sustain combustion, chamber temperature is low and this is the reason why cold gas thrusters produce less thrust than conventional chemical engines. The following table shows 𝐼𝑠𝑝 values for different gases commonly used with cold gas thrusters. 2 Development 10 4: Note that this equation is valid for the condition of ideal expansion. More on this can be found in Section 2.3 Cold Gas Molecular weight M (u) Theoretical Isp (sec) Density (g/𝑐𝑚3) at 241 bar 𝐻22.0 296 0.02 𝐻𝑒 4.0 179 0.04 𝑁𝑒 20.2 82 0.19 𝑁228.0 80 0.28 𝑂232.0 - - 𝐴𝑟 40.0 57 0.44 𝐾𝑟 83.8 39 1.08 𝑋𝑒 131.3 31 2.74 𝐶𝐶𝑙2𝐹2120.9 46 Liquid 𝐶𝐹488.0 55 0.96 𝐶𝐻416.0 114 0.19 𝑁𝐻317.0 105 Liquid 𝑁2𝑂44.0 67 Liquid 𝐶𝑂244.0 67 Liquid Table 2.1: Cold gas propellant performances for different gases at 25 º C, extracted from [8] If we compare the previous values of 𝐼𝑠𝑝 to those of conventional chemical rocket engines, which typically range in between 200s and 500s, we can observe that they are considerably lower. Additionally, if we consider that thrust is directly proportional to 𝐼𝑠𝑝 , we can expect much lower values of thrust from a cold gas thruster: 𝐹𝑡ℎ =¤ 𝑚·𝐼𝑠𝑝 ·𝑔(2.6) where ¤ 𝑚 is the propellant mass flow rate 4 . This fact of expecting low values of thrust drives a new design requirement: Design Requirement 2.4 Reducing weight must always be considered throughout the design process of the vehicle. Because of the low value of 𝐼𝑠𝑝 , the thrust generated is expected to be low and therefore the vehicle’s wet mass has to be reduced whenever possible to help ensure a successful vertical landing. Additionally, as will be seen in detail in Section 3.1, the thrust of a cold gas thruster is directly related to the tank pressure. This means that as the tank empties, thrust will diminish. 2.2 Identification and Selection of Options This section sets out to consider the possible options for propellants and active stabilization. The various considered options will be presented and then the most appropriate will be determined employing the decision making criteria. 2 Development 17 Figure 2.10: Render of initial aerobrake model. Own elaboration Figure 2.11: CFD analysis of initial aerobrake model. Own elaboration 2.3 Initial Parameters This section sets forth two Matlab simulations developed in order to determine a series of initial parameters required for proper sizing of the propulsion system, choosing drop height and maximum wet mass. In order to do so, a definition of the flight profile is required in advance. 2.3.1 Flight Profile The flight profile can be described with six phases: IPhase 01: The launching of the vehicle. In this case launching will be the releasing of the vehicle from a predetermined height. IPhase 02: Deployment of aerobrakes. Vehicle is still accelerating. IPhase 03: Vehicle reaches terminal velocity when the drag generated is equal to the gravitational force. IPhase 04: cold gas thruster is fired and vehicle starts to decelerate and actively stabilize. IPhase 05: Landing legs are deployed. IPhase 06: Vehicle touches down with velocity equal to 0. Having defined the flight profile we can now develop the simulation algorithms. 2.3.2 Required Thrust Algorithm This algorithm is developed to describe the flight and determine the required thrust as a function of drop height and vehicle wet mass. This algorithm takes into consideration the effects of drag generated by the rocket body and aerobrakes and in order to do so it was first required to run a CFD simulation to determine drag coefficients. The CFD simulation was performed on SolidWorks’s Flow Simulation add-on. The simulation was run considering incompressible flow since the Mach number was not expected to get close to 0.3, where the flow starts to behave subsonically and incompressibility can’t be supposed [13]. 3D models of the aerobrakes and vehicle body with the expected final form factor and surface area were modeled and introduced into the simulation environment. A more detailed explanation of how the simulations were carried out can be found in Section 3.3.1 (CFD Simulation) on page 52. It’s important to note that the results of these simulations are only preliminary since they were carried out in early stages of the project where various sizing parameters were yet to be determined. The drag coefficients determined by the simulations are: 2 Development 18 Figure 2.12: CFD analysis of initial vehicle body model. Own elaboration Aerobrake Vehicle body 𝐶𝐷1.488 0.891 Table 2.3: Drag coefficients of initial aerobrake and vehicle body simulations Once the CFD analysis has been performed, the algorithm can be developed. It runs an iterative process where each iteration calculates the velocity at impact. The process converges on a value of thrust that returns a velocity of zero when touching down. 2.3.2.1 Algorithm Flowchart and Results A summary of the Required Thrust algorithm developed with Matlab is presented in the form of a flowchart in Figure 2.13 below: 2 Development 19 Start Global numeric and fisical variable definition (Cd, dt, g, iginition height...) Initial calculations for t=0s (a, v, h, drag...) t=t+dt Have aerobrakes been deployed? Calculate aerobrake drag (with v at t-dt) Yes Ha thrust began? Calculate body drag (with v at t-dt) Total drag=body drag Total drag= body+aerobrake drag Net force=m*gtotal drag - thust No Thrust=0 Calculate new values of a, v and h Is h=0? (Touchdown) Current v = v at t-dt Required thrust = current T Yes No Is there a new mass value? Update mass value Yes Is there a new height value? Update height value No Yes Print results End No Figure 2.13: Required thrust Matlab algorithm flowchart 2 Development 20 11: Pulse Width Modulation is a method used to convert direct current into AC by chopping the DC current into discrete parts of different width. It’s important to note that this algorithm considers that once thrust begins at phase 04 of the flight profile, it remains constant until touchdown. In reality this will not be the case since thrust will be varied according to the needs of each instance by firing short pulses. The pulse method can emulate variable thrust in a similar way that PWM 11 can can vary the average power delivered by an electrical signal. In addition it’s worth mentioning that when the aerobrakes are deployed the total drag is calculated as the sum of the body’s and the aerobrakes drag independently. This is not completely accurate because the interactions in between the body and the aerobrakes will affect the drag values, but as an initial model this method will suffice. Furthermore, mass is also considered to be constant. This is not entirely precise reason being that the vehicles mass diminishes in time as it ejects propellant. Having said that, as will be seen in the next section, the propellant mass is approximately 50g. Therefore the vehicle’s mass is considered to be constant. The following figures show the results obtained by the algorithm. Figure 2.14 considers a drop height of 20m while Figure 2.15 considers 40m. 0 0.5 1 1.5 2 2.5 3 3.5 time (s) -15 -10 -5 0 5 10 15 20 Velocity, acceleration and height for a mass of 0.5kg. Required thrust = 6.3735N Velocity (m/s) Acceleration (m/s2) Height (m) 0 0.5 1 1.5 2 2.5 3 time (s) -20 -15 -10 -5 0 5 10 15 20 Velocity, acceleration and height for a mass of 1kg. Required thrust = 17.4313N Velocity (m/s) Acceleration (m/s2) Height (m) 0 0.5 1 1.5 2 2.5 time (s) -20 -15 -10 -5 0 5 10 15 20Velocity, acceleration and height for a mass of 1.5kg. Required thrust = 30.9547N Velocity (m/s) Acceleration (m/s2) Height (m) 0 0.5 1 1.5 2 2.5 time (s) -20 -15 -10 -5 0 5 10 15 20 Velocity, acceleration and height for a mass of 2kg. Required thrust = 45.6769N Velocity (m/s) Acceleration (m/s2) Height (m) Figure 2.14: Required thrust algorithm results for a drop height of 20m. Each subplot represents a different vehicle wet mass. Velocity, acceleration and height are plotted over time. 2 Development 21 12: The aerobrakes have been set up to be deployed when the vehicle hits 95% of the initial drop height. As can be seen in the plots, the flights start off with relatively constant acceleration equal to g. As soon as the aerobrakes deploy 12 the acceleration starts to diminish with different slopes according to the vehicles mass. When the engine is ignited (programmed to do so at 30% of the initial height), acceleration drastically drops and turns negative. By doing so the vehicle begins to decelerate. As of this point the acceleration reduces in modulus. This is because as the vehicle slows down, the drag generated by the aerobrakes diminishes. Quite intuitively, the greater the wet mass, the more thrust is required and greater maximum accelerations are experienced. 012345678 time (s) -20 -10 0 10 20 30 40 Velocity, acceleration and height for a mass of 0.5kg. Required thrust = 5.1865N Velocity (m/s) Acceleration (m/s2) Height (m) 0 1 2 3 4 5 time (s) -20 -10 0 10 20 30 40 Velocity, acceleration and height for a mass of 1kg. Required thrust = 12.6988N Velocity (m/s) Acceleration (m/s2) Height (m) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time (s) -20 -10 0 10 20 30 40Velocity, acceleration and height for a mass of 1.5kg. Required thrust = 22.7901N Velocity (m/s) Acceleration (m/s2) Height (m) 0 0.5 1 1.5 2 2.5 3 3.5 4 time (s) -20 -10 0 10 20 30 40 Velocity, acceleration and height for a mass of 2kg. Required thrust = 34.6738N Velocity (m/s) Acceleration (m/s2) Height (m) Figure 2.15: Required thrust algorithm results for a drop height of 40m. Each subplot represents a different vehicle wet mass. Velocity, acceleration and height are plotted over time. Comparing these plots with the plots from Figure 2.14 a few differences can be observed. First of all, and most surprisingly is to do with the required thrusts. Initially, the hypothesis was that with higher drop heights the vehicle would accelerate more and thus require more thrust to bring to a standstill. Surprisingly the results show the opposite. The required thrust for a drop height of 40m is always smaller than that required for a drop height of 20m, no matter the weight. In order to better represent this behaviour the algorithm was modified to plot 2 Development 22 13: An initial estimation of vehicle mass was performed by adding up the approximate masses of the components that were thought to be needed. required thrust different drop heights as a function of mass. The results are presented in Figure 2.16 below. 0.511.52 mass (kg) 0 10 20 30 40 50 60 Required thrust (N) Drop height=10m Drop height=20m Drop height=30m Drop height=40m Figure 2.16: Required thrust for different values of drop height as a function of vehicle mass. The plots show clearly that the greater the vehicle mass the more thrust is required but additionally they demonstrate that greater heights require less thrust for a same value of vehicle mass. The reason behind this peculiarity is that higher dropping heights allow for the vehicle to get closer to terminal speed, letting drag do more of the work. The greater the vehicle’s mass the more pronounced this effect it. The information that this conclusion gives us not ideal. Preferably, the vehicle must reach terminal velocity before firing it’s thruster. If the drop height is not high enough, the vehicle doesn’t have enough time to reach terminal velocity and the thruster has to fire prematurely which is less efficient. According to the results, the only case where terminal velocity is reached is for a drop height of 40m with a mass of 0.50kg. This is not realistic since vehicle mass is expected to be in between 1 and 1.50kg13 , not to mention that finding a launch location of 40 meters would be particularly difficult due to urban and building safety regulations. This information is derived into a design constraint that must be considered. Design constraint 2.1 Terminal velocity will not be achieved due to the nonavailability of launch locations with the required drop height. This means that in the scope of the project more thrust will be required compared to what would be needed in reality where the vehicle would reach terminal velocity. As an exercise, the algorithm is modified to calculate the required drop height in order to reach terminal velocity for different vehicle masses. Another conclusion which can be drawn from this algorithm is the effect of the ignition height on the required thrust. As a means to accomplish 2 Development 23 Vehicle mass [kg] Required drop height [m] Required thrust [N] 1.00 60.00 11.04 1.25 75.00 13.80 1.50 95.00 16.32 Table 2.4: Required drop heights in order to reach terminal velocity for different vehicle masses. The last columns represents the required thrust for zero velocity touchdown considering thruster ignition at 30% of the drop height. 14: The launch would have to performed on private property to insure no harm is caused to bystanders nor any property damage. Also, the launch spot would need to have enough clearance in order to safely drop the vehicle without it impacting any obstacles on the way down. Finally, the ground directly bellow the launch site must be flat and free of any obstacles. These constraints limit the plausible launch locations greatly. this the algorithm is modified yet again and these are the results: 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ignition height (adimensional) 10 20 30 40 50 60 70 Required thrust (N) Drop height=20m Drop height=30m Drop height=40m Figure 2.17: Required thrust as a function of adimensional ignition height (ignition height/drop height) for different initial drop heights at constant vehicle weight of 1kg. The conclusion drawn from these results is that the earlier the thruster is fired, the less thrust is required. The problem is that the propulsion system probably wont be able to store enough propellant for burning throughout the entirety of the flight, which as seen in the figures above is predicted to be a flight of in between 2.50 and 5.00 seconds. A sweet point will have to be determined once the propulsion system is built and the thrust curves are obtained. Assuming that the expected wet mass is to be around 1 and 1.5.00kg and that the maximum drop height achievable is approximately 20m 14 , we can use these results to derive a thrust design requirement. The value defined includes a leverage margin to compensate for elements not considered in this algorithm, for example, the TVC horizontal component of the thrust used for stabilizing, atmospheric conditions and most importantly the fact that the velocity at impact does not need to be zero . An acceptable impact velocity would range between 3 and 4.5m/s. By accepting a 3m/s impact velocity the required thrust drops 4N on average. Design Requirement 2.5 The vehicle must be capable of producing at least 20N of thrust. 2 Development 24 Design Requirement 2.6 The vehicle’s wet mass should not exceed 1.50kg. The Matlab code that runs the algorithm can be found in Annex A.1. 2.3.3 Burn Algorithm The following algorithm is developed to correctly size the components that make up the propulsion system. In order to do so, it incorporates rocket, thermodynamic and flow equations applicable to a cold gas thruster which will be described hereafter. The algorithm takes into consideration the following suppositions: I Air is considered to be a real gas and therefore the Z compressibility factor is exploited in order to take into consideration the deviation the gas presents with respect to an ideal gas. IThe flow is isentropic IThe gas expansion is considered to be ideal IThe Joule-Thomson effect is not considered. 2.3.3.1 Flow Equations As shown in Section 2.1.3 (Cold Gas Thruster) the thrust produced by a cold gas thruster can be described with equation 2.3: 𝑇=¤ 𝑚𝑢2+ (𝑃2−𝑃3)𝐴2 where ¤ 𝑚 is the mass flow rate, 𝑢2 the escape gas velocity, 𝑃2 the gas pressure at the exit, 𝑃3 the ambient pressure and 𝐴2 the cross section area of the exit. Taking a look at the pressure term of this equation one can see if 𝑃2 is less than 𝑃3 , the resulting thrust is decreased. Not so intuitively, having 𝑃2 greater than 𝑃3 does not increase thrust, as a matter of fact it reduces it due to the fact that 𝑢2 is not as high as it could be. With these opposing effects rocket thrust is maximized for the condition 𝑃2=𝑃3 , meaning the exit pressure of the exhaust is equal to the ambient pressure[14] [14]: Nothnagel et al. (2010), ‘Development of a cold gas spacecraft emulator system for the TALARIS hopper’ . This condition is known as optimum ideal expansion and it simplifies the calculations. It is common and convenient to define an equivalent exhaust velocity 𝑢𝑒𝑞: 𝑢𝑒𝑞 =𝑢2+𝑃2−𝑃3 ¤ 𝑚𝐴𝑒(2.7) in such a way that equation 2.3 can be written as: 𝐹𝑡ℎ =¤ 𝑚𝑢𝑒𝑞 (2.8) For the condition of ideal expansion 𝑢2=𝑢𝑒𝑞 2 Development 25 0510 15 20 25 30 [º] 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Figure 2.18: Lambda nozzle correction factor. Own elaboration By recalling equation 2.4, the escape velocity can be related to specific impulse: 𝐼𝑠𝑝 =𝑢2 𝑔0 and then equation 2.8 can be turned into 2.6 from Section 2.1.3: 𝐹𝑡ℎ =¤ 𝑚·𝐼𝑠𝑝 ·𝑔 Due to the inherit geometries of convergent-divergent nozzles, a nozzle correction factor must be considered: 𝜆=1+𝑐𝑜𝑠𝛼 2(2.9) where 𝛼 is the divergent cone half-angle. Having such a geometry implies that not all the exhaust is ejected normally to the exit cross section. Some thrust is lost as a side component. Figure 2.18 displays a graph represents the nozzle efficiency as a function of divergent cone half-angle. The cone half angle has a typical value of 15 º which provides a good compromise on the basis of weight, length and performance [15] [15]: Robert A (2012), Basics of Space Flight: Rocket Propulsion Including the nozzle correction factor, thrust can be expressed as: 𝐹𝑡ℎ =𝜆·¤ 𝑚·𝐼𝑠𝑝 ·𝑔(2.10) All that is left to determine is the 𝐼𝑠𝑝 which is affected by nozzle geometry and the thermodynamic state of the gas. Equation 2.5 from Section 2.1.3 describes and includes these affects: 𝐼𝑠𝑝 =1 𝑔v u t2𝛾 𝛾−1·𝑅𝑠𝑝 ·𝑇𝑐"1−𝑃𝑒 𝑃𝑐𝛾−1 𝛾# where 𝑅𝑠𝑝 is the specific gas constant ( 𝑅/𝑀 ), 𝛾 the propellant heat capacity ratio which is equal to 1.4 for air, 𝑇𝑐 is the combustion chamber temperature and 𝑃𝑒 𝑃𝑐 the external-chamber pressure ratio, characteristic to the nozzle geometry. This equation shows that having greater values of specific gas constant, chamber temperature and chamber pressure favour specific impulse. The specific gas constant is considered constant, and by incorporating a pressure regulator into the propulsion system so can the chamber pressure. What can’t be considered constant is the chamber temperature despite the fact that no combustion is housed in a cold gas thruster. The reason behind this is the Joule-Thomson effect. 2 Development 26 Figure 2.19: Joule-Thomson inversion curves for common cryogenic fluids a) Methane; b) Air; c) Neon; d) Hydrogen; e) Helium. Extracted from [16]. 2.3.3.2 Thermodynamic Equations When a real gas is expanded insenthalpically like in a convergentdivergent nozzle, it experiences a change in temperature due to the Joule-Thomson effect. Whether the gas warms or cools is up to the sign of the Joule-Thomson coefficient which is the partial derivative of temperature with respect to pressure at constant enthalpy: 𝜇𝐽𝑇 =𝜕𝑇 𝜕𝑃𝐻 (2.11) As stated in Section 2.2.1, the projects expected range of working temperatures (250-300K) are located within the air’s J-T inversion curves. 15 15: Curves formed by the points at which the Joule-Thomson coefficient is equal to 0 as shown in Figure 2.19. This means that 𝜇𝐽𝑇 is positive and therefore the air cools as a result of insenthalpic expansion[16] [16]: Windmeier et al. (2013), ‘Cryogenic Technology’ . To sum up, due to the Joule-Thomson effect as the air from the tank is depleted, the chamber temperature will decrease which in turn decreases 𝐼𝑠𝑝 and consequently the thrust as well. Multiple attempts were carried out to include this effect in the algorithm but none were successful. The results obtained always differed greatly from the results of experimental observations carried out. This outcome pushed the decision to not include the Joule-Thomson effect in the algorithm, acknowledging the fact that reduction in thrust due to gas cooling would not be modeled, calling for attention towards ’room for error’ when selecting components. As a means to describe the tank depletion the ideal gas law is necessary. Since the algorithm considers air to be a real gas, the Z dimensionless compressibility factor is applied: 𝑃=𝑍𝜌𝑅𝑠𝑝𝑇(2.12) The Z factor varies in function of temperature and pressure. Experimental data of air’s compressibility factor [17] [17]: Kazavcinskij (1971), ‘Thermophysical properties of air and air components’ is incorporated into the algorithm. 2.3.3.3 Flow Equations The propulsion system will include a normally closed solenoid valve. In order to properly size pneumatic and hydraulic valves, flow factors are used to evaluate their efficiency at allowing fluid flow by defining the flow rate in 𝑚3/ℎ of water at a pressure drop across the valve of 1 𝑘𝑔/𝑐𝑚2 , considering that the valve is completely open. The flow factor (𝐾𝑣) can be calculated according to the following equation[18] [18]: Baker Hugues (2019), Masoneilan Control Valve Sizing Handbook : 𝐾𝑣=¤ 𝑚 𝑁·𝐹𝑝·𝑌·p𝑥·𝑃1·𝛾1 ·0.87 (2.13) where I𝑥is the pressure drop across the valve (Δ𝑃/𝑃1). 3 Design and Construction 33 Figure 3.1: Constructed pneumatic propulsion system and its components. 1) High pressure tank; 2) Pressure regulator; 3) Manual shutoff valve; 4) Line quick release connector; 5) Solenoid valve; 6) High pressure air lines IHigh pressure lines: tubing capable of withstanding high pressures to connect the different elements that compose the pneumatic system. INozzle: used to expand and accelerate the exhaust. In conformity with the findings of Section 2.2.1 (Propellant Selection), the option for refilling will be via a scuba tank, which is pressurized to 20MPa. This decision was convenient because this practice is typical in the paintball world, opening a door to cheaper pneumatic components that otherwise would be out of reach because of their cost. Following the parameters determined in Section 2.3.3 (Burn Algorithm) the component selection process can begin. The tank that was selected is a 0.21L aluminium paintball tank rated for 3000psi (20.68MPa), which at 0.36kg is lighter than a steel tank rated for the same pressure. Originally the tank was a 0.40L, but eventually it was decided to go with the smaller tank in order to reduce weight. More on the topic will be explained in this chapter. When it came to the pressure regulator, design requirement 2.3 of obtaining the highest 𝐼𝑠𝑝 possible was contemplated. To obtain high 𝐼𝑠𝑝 , the pressure at the output of the regulator has to be as high as possible, bearing in mind the maximum operational pressures that the valves and tubing can withstand. Regulators with up to 850psi (5.86MPa) output were also sourced but had to be disregarded. In the end the output pressure had to be compromised to a value of 300psi (2.07MPa), a pressure that allows us to find compatible components on the market. The paintball Soger Gf HP regulator (3000psi-300psi) was chosen, a pressure regulator that reduces a maximum pressure of 20.68 to 2.07Mpa, a reduction factor of 10. The pressure regulator also includes a fill valve and two pressure relief valves (PRV) , one for each side of the regulator. To be precise the PRVs are burst disks rated for 1800psi and 5000psi which when fed pressures that surpass these values, they burst and rapidly release the air. When filling the tank, as a safety precaution the bursts disks should never point in the direction of the user. The regulator also incorporates a pressure gauge which comes in handy for determining the tank pressure and to help avoid overfilling. An advantage with going with the paintball components is that threads are standardized, meaning that the regulator can be mounted directly on to the tank. A stop valve was selected so it could be mounted on the other side of the pressure regulator. The main disadvantage of using paintball components is their lack of proper data sheets, which meant that important parameters such as their flow factors are unknown. This turned out to be a major flaw for the propulsion system, but more information on this will be detailed hereafter. As for the solenoid valve, the Festo VZWD-L-M22C-M-G18-15-V-1P430 normally closed valve was chosen because of its lightweight design, coming in at 0.176kg. The valve has a maximum operating pressure of 3MPa, which is more than enough to withstand the pressures of the LP (low pressure) side of the system. Another reason why this valve was chosen was the coil powering voltage of 24V. Most high pressure valves on the market require 220V, a value that wouldn’t be achieved 3 Design and Construction 34 Component Weight [kg] Tank 0.36 Regulator 0.18 Shutoff valve 0.06 Solenoid 0.18 Total 0.928 Table 3.1: Pneumatic propulsion system weights. 1: BSPP stands for British Standard Pipe Parallel thread and which is a set of technical standards for threads. In this case for parallel threads. with the designed circuit but 24V can be achieved with the use of a buck-boost converter. Another aspect this solenoid had going for it was the small commutation delays of 25ms for on and 10ms for off. This would allow for very fast bursts that are required to simulate thrust throttling. Concerning the flow parameters, the solenoid was selected taking into consideration the nominal flow (Q) provided by the data sheet. With a value of 95L/min, the first version of the Burn algorithm deemed the valve capable of allowing sufficient mass flow in order to achieve the required 20N of thrust. With testing it was later determined that nominal flow could not be used to size the valve properly and as a result the chosen solenoid valve constricted the flow too much. This can be clearly explained in terms of flow factors: as stated in design requirement 2.7, the flow factor must be at least 0.381 𝑚3/ℎ , whilst the selected valve has a 𝐾𝑣 of merely 0.09 𝑚3/ℎ . More on this issue will be explained shortly. 4mm Polyurethane tubing with an internal diameter of 2.70mm was selected for the HP connection lines because if its relatively small bend radius compared to other options such as nylon. The tubing can support pressures of up to 2.20MPa, making it adequate for the LP side of the system. In order to connect the tubing in between components quick release connectors with BSPP 1/8"1were implemented. Table 3.1 summarizes the wight of the system’s components. Note that the overall mass of the propulsion system, when compared to the maximum wet mass requirement, is quite high. This puts an emphasis on taking the reduction of weight very seriously from now onward. A diagram of the propulsion system and its components is depicted in Figure 3.2 Pressure gauge Air source Filter Check valve Air tank Relief valve Relief valve Pressure regulator Stop valve NC Solenoid valve Nozzle HP side 20MPa LP side 2MPa Figure 3.2: Pneumatic propulsion system diagram made with SMCDraw [20] 3 Design and Construction 35 Figure 3.3: Thrust test bench CAD render. 1) Nozzle mount; 2) Nozzle mount support; 3) Load cell; 4) Base 3: 𝐼2𝐶 is a commonly used short distance intra-board communication protocol. 3.1.1 Thrust Test Bench With the aim of being able to test the amount of thrust the propulsion system is capable of producing and for generating thrust curves to analyse, the need for creating an apparatus to do so emerged. To design this test bench the following requirements are identified: IIt must be capable of saving the data captured. IIt needs to be able to resist at least 20N of thrust. I The design must facilitate a way to mount and dismount different nozzles. In order to realize this need it is decided to go for a load cell with an integrated Wheatstone Bridge 2 2: The integration of a Wheatstone bridge with a load cell allows for measurement of the load cell’s deformation when force is applied using strain gauges. This deformation can then be processed and transformed into force. . Many types and sizes of load cells are available on the market, and one rated for 20kg is selected. The load cell has to be mounted in a specific way in order to get correct readings, for this reason a base consisting of 3 parts was designed on SolidWorks. During the design process the nozzle interchangeability was taken into account by designing a mount to fix nozzles into place using three M5 bolts and nuts. Drawings of these CAD designs can be found in the Drawings document section D.6. As for the data saving aspect, a module housing the HX711 24-Bit Analog-to-Digital Converter is selected. This module converts the analog output of the Wheatstone bridge and converts it to a digital output that can be interfaced with an Arduino using an 𝐼2𝐶 protocol 3 for signal processing using the library that the manufacturer provides. Once the load reading is obtained, the Arduino can establish a serial connection with a PC and the data can be saved. Figure 3.4: Thrust test bench setup. The Arduino triggers the solenoid valve (inferior-center) and air then flows through the nozzle (green part mounted on test bench) and the data is recorded. A small Arduino program is developed for setting up both 𝐼2𝐶 and serial connections, calibration and signal processing using the library provided. Find a copy of the code in Annex B.1. In order to make sure that the readings were correct, a series of tests were performed using different objects with known weight. The test bench was able 3 Design and Construction 36 to determine their weight with a margin of error of about ± 0 . 001 𝑘𝑔 , considered more than valid for the current application. Whilst performing these tests it was realized that the readings had a considerably large settling time of 180ms. Considering that the burn time would only be around 2500-3000ms, the settling time is considered unacceptable. Fortunately, according to the HX711 data sheet, the default sampling rate is 10SPS (samples per second) but can be raised to 80SPS with a physical modification to the board consisting in pulling up pin 15. Unfortunately, upping the sampling rate comes at the cost of being more susceptible to noise but the compromise was deemed beneficial in the long run. 3.1.2 Nozzles, Tests and Troubleshooting In order to obtain some initial thrust results the nozzle needs to be designed. As a first iteration, a conical convergent-divergent nozzle is selected because of its FDM manufacturing simplicity. In order to design the nozzle a few key concepts need to be understood beforehand. As implied by the name, convergent-divergent nozzles are composed of two concentric nozzle sections, the first convergent and the second divergent. The point where the latter meet is known as the throat and it has the smallest cross sectional area of the nozzle. When sizing the nozzle, the objective is to have the flow accelerate no matter what the flow Mach number is. To physically produce this design it is important to bear in mind that a convergent nozzle accelerates subsonic fluid, while supersonic flow is accelerated by a diverging nozzle. On that account, the most efficient way of accelerating flow through a convergent-divergent nozzle is to have sonic flow at the throat (Ma=1). This condition is known as choked flow and can be obtained with proper sizing. The main parameter when it comes comes to sizing nozzles is the expansion ratio, which is the relation of the nozzle exit 𝐴𝑒 area to the 𝐴𝑡 throat area. Using the condition of nozzle choking the expansion ratio can be determined with the following equation derived from the continuity equation and the conservation of energy equation: 𝜀=𝐴𝑒 𝐴𝑡 =1 𝑀𝑒v t2 𝛾+11+𝛾−1 2𝑀2 𝑒𝛾+1 𝛾−1 (3.1) where 𝑀𝑒 is the nozzle exit Mach number, which for choked flow is given by the next equation: 𝑃𝑐 𝑃𝑒 =1+𝛾−1 2𝑀2 𝑒𝛾 𝛾−1 (3.2) where 𝑃𝑐 is the chamber pressure, assumed to be the LP side value of 2.07MPa; and 𝑃𝑒 is the exit pressure which, if ideal expansion is supposed, is equivalent to 101325Pa. The pressure ratio gives an exit Mach number which in turn provides a expansion ratio. 3 Design and Construction 37 Component Smallest diameter [mm] Regulator 1.50 Quick release fittings 3.18 Stop valve 3.22 Solenoid 4.07 Tubing 2.70 Table 3.2: Propulsion system constricting diameters. Figure 3.5: Render of first nozzle iteration. The design incorporates a base to be able to mount it to the thrust test bench. The next geometric parameter required to define the nozzle geometry is the cross section area of the throat. The way it is determined is by abiding to the following requirement: in order for the flow to choke at the nozzle throat, 𝐴𝑡 must be the smallest cross sectional area of the whole propulsion system. If this condition is not met, the flow might choke elsewhere in the system and as a result disregarding the effect of the nozzle. As a result the most constricting diameters of the propulsion are determined either manually or by looking up the data-sheets. As stated in Table 3.2, the most constricting section of the propulsion system belongs to the solenoid valve. Therefore, a throat diameter of 1.400mm is selected. The last parameter needed is the divergent cone half-angle 𝛼 , which in Section 2.3.3 was determined to be 15 º . The geometry of the converging section does not have to be defined exactly since the choke condition is set by the expansion ratio. In a way, flow "information" cannot travel beyond the choked throat,meaning its geometry is irrelevant and can be set to best suit the projects needs, which is to adapt to the quick release fittings. The dimensions of the first nozzle iterations are detailed in Figure 3.6 below. A drawing of the CAD model can be found in Drawing document section D.4: A A 2.39 1.40 8.80 15° 45° 9.00 5.55 SECTION A-A A A B B C C D D 6 6 5 5 4 4 3 3 2 2 1 1 NAME: DATE: ASSEMBLY: SCALE DESCRIPTION: MATERIAL: DRAWN BY: PROJECT: STABILIZATION SYSTEM OF A ROCKET WITH REENTRY AND VERTICAL LANDING CAPABILITIES PLA SYLVAIN WALSH BRIEF ESCRIPTION OF THE PART BRIEF ESCRIPTION 1:1 ASSEMBLY PART NAME 29/05/21 SOLIDWORKS Educational Product. For Instructional Use Only. Figure 3.6: Initial nozzle dimensions and geometry. Dimensions are in mm. The following table recollects the key parameters if the first iteration of the nozzle: 𝑀𝑒2.61 Throat area 𝐴𝑡[𝑚𝑚2] 1.539 Expansion ratio 𝜀2.92 Divergent cone half-angle 𝛼15º Exit area 𝐴𝑒[𝑚𝑚2] 4.49 Divergent cone length [mm] 1.550 Table 3.3: Initial nozzle geometrical parameters Once the nozzle is designed, it is manufactured using FDM and a thrust test is executed, the results of which are shown in Figure 3.7 on the next page: 3 Design and Construction 38 0102030405060 Time (s) -0.5 0 0.5 1 1.5 2 2.5 Thrust (N) Initial nozzle thrust curve Figure 3.7: First iteration of the nozzle thrust curve. This test was carried out with an initial tank pressure of 20.00MPa The results obtained are quite controversial to the project. The following observations were made: IMaximum thrust: The above thrust curve shows clearly that the required thrust of 20N is not achieved, not by a long shot. To be precise, the maximum thrust obtained is only 10% of the required, a value that definitely won’t be able to decelerate the vehicle enough. Ergo in order to have a chance at being able to vertically land, this issue must be examined. IBurn time: The burn time of 50s is a lot more than expected. As a matter of fact almost 19 times greater than what is predicted with the burn algorithm. The cause of this issue is hypothesized to be a constriction in the mass flow, not letting air escape the tank fast enough and therefore increasing burn time as well as decreasing maximum thrust. INoise: There is a considerable amount of noise in the readings, especially in between t+10s and t+30 seconds. The excess in noise is believed to be a consequence of upping the sampling rate of the load cell chip to 80SPS, as talked about in Section 3.1.1. The noise could be reduced with further signal processing but it’s not considered an issue for the interpretation of the plots. 3 Design and Construction 39 Figure 3.8: CAD model of one of the nozzle iterations. 𝜀 : 2 . 92; throat diameter: 3mm; half-angle: 4 º ; divergent cone length: 14.75mm. A drawing of this nozzle can be found in the Drawings document section D.4. IThrust slope: The last intriguing aspect of this thrust curve is the fact that the thrust is not constant. The use of a pressure regulator should in theory keep the chamber pressure constant meaning that thrust should be practically constant, at least until the tank pressure equals the regulator output pressure, at which point the chamber pressure reduces as the rest of the air in the tank is depleted. In order to test the last statement, the output of the regulator is connected to a pressure gauge and measures are taken for different tank pressures. As expected, the regulator output pressure kept at a constant 2MPa. The only other factor that could be reducing the thrust is the decrease of the chamber temperature due to the Joule-Thomson effect. Unfortunately, a temperature probe couldn’t be obtained so the only way of confirming the cooling was by touch. To do so, a test burn was performed and then the different components were felt. The temperature reduced noticeably, up to the point that condensation was formed on the regulator and solenoid valve. Having said that, opportunely it seemed that the temperature didn’t fall bellow the -10 º C minimum operating temperature of the solenoid valve. To summarize, the reduction in thrust seems to be caused as a consequence of the decrease of 𝐼𝑠𝑝 due to the Joule-Thomson effect that lowers the chamber temperature. With the purpose of figuring out why such poor thrust values are obtained, thrust equation 2.3 is broken down: 𝑇=¤ 𝑚𝑢2+ (𝑃2−𝑃3)𝐴2 Obviously, lesser mass flow and exhaust velocity will decrease thrust output. As for the pressure term, if 𝑃2 is less than 𝑃3 , the resulting thrust is decreased. Not so intuitively, having 𝑃2 greater than 𝑃3 reduces thrust due to the fact that 𝑢2 is not as high as it could be. With these opposing effects rocket thrust is maximized for 𝑃2=𝑃3 , the ideal expansion condition. Both the pressure term and exhaust velocity ( 𝑢2 ) are determined according to, in between other parameters, the nozzle geometry. This means that a possible culprit could be the nozzle sizing. With the means of testing this hypothesis multiple CAD models are created varying geometric parameters such as the expansion ratio ( 𝜀 ), the cone half-angle, cone lengths, and throat area. These new designs are put to the test in order to see if they perform any better. 3 Design and Construction 40 Figure 3.9: Nozzle iterations fabricated using FDM, with varying geometrical parameters. We can establish that the test conditions are not exactly the same for all nozzles. This is because the initial tank pressure isn’t always the same due to the refilling method which uses a scuba tank to refill the propellant storage tank. The issue is that the scuba tank refill until the pressures are equalized, but as tests are performed, the pressure of the scuba tank depletes meaning the initial tank pressure drops after each test. An experimental calculation was made in order to figure out the depletion rate, and it turned out to be around 50psi (350.00KPa) per refill. This fact called for when comparing thrust gains, if the variation was small (less than 10%), the results wouldn’t be considered to be an improvement. After many iterations and tests, no considerable improvement is obtained , which leads to the belief that the poor thrust results are a consequence of mass flow constriction throughout the propulsion system, which is clearly related to the burn time: the longer the tank takes to deplete its propellant mass, the lower mass flow the system presents. The fact that the burn times are approximately 50s, which as stated above is 19 times over what the burn algorithm predicts as required for the production of 20N of thrust, supports consistently the hypothesis that the mass flow is being constricted. In order to test this hypothesis, a series of thrust tests are carried out to evaluate the effects of each component. First the propulsion system with the solenoid valve is tested, followed by a test without the solenoid valve but including the polyurethane tubing; and finally a test including only the regulator and stop valve. The objective of these experiments is finding the amount of time it takes for thrust to reach 50% of its initial value, a value that shall be called 𝜏50 time constant. Note that the tests are performed at different initial tank pressures, meaning the maximum thrust value is not of interest, only the time constant. 3 Design and Construction 41 0246810 12 14 Time (s) -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Thrust (N) Regulator, stop valve, tubing and solenoid thrust curve 50 Thrust (N) 50 = 8.915s 50%T = 0.67965N Figure 3.10: Regulator, stop valve, tubing and solenoid thrust curve. Initial tank pressure: 14MPa. 0246810 12 14 16 Time (s) 0 1 2 3 4 5 6 Thrust (N) Regulator, stop valve and tubing thrust curve 50 Thrust (N) 50 = 6.156s 50%T = 2.6456N Figure 3.11: Regulator, stop valve and tubing thrust curve. Initial tank pressure: 20.00MPa. 3 Design and Construction 42 Test 𝜏50 [s] Regulator + stop valve + tubing + solenoid 8.92 Regulator + stop valve + tubing 6.16 Regulator + stop valve 2.375 Table 3.4: Time constants for the mass flow constriction experiments. 4: The flow coefficient measures the volumetric flow through a system under specific pressure conditions. The parameter does not take into consideration the high working pressures of the propulsion system, causing for great deviations in the results. 0510 15 Time (s) 0 1 2 3 4 5 6 7 Thrust (N) Regulator and stop valve thrust curve 50 Thrust (N) 50 = 2.375s 50%T = 3.2462N Figure 3.12: Regulator and tubing thrust curve. Initial tank pressure: 14.00MPa. Note that Figure 3.11 and Figure 3.12 represent the results belonging to the tests performed without a solenoid valve, which in effect required manual triggering of the stop valve in order to begin the burn, hence the irregularities for the first milliseconds of the burn. In order to compensate for the time required to trigger the stop valve, a time offset is applied to the time constants of the figures in question. Table 3.4 shows the time constants obtained. This experiment clearly validates the hypothesis of mass flow constriction. The regulator and stop valve alone vents the propellant much faster than the system that utilizes tubing and a solenoid valve, indicating that constriction is present. Taking a look at the 𝜏50 values it’s easy to identify the solenoid valve as the most constricting component. At this point it was realised that an error had been made pertaining to the sizing of the components, specifically using the nominal flow 4 provided by the data sheets, instead of the flow factor, as detailed in Section 2.3.3. Having realized this mistake, the burn algorithm was corrected to work with flow factors instead and design requirement 2.7 which specifies a minimum flow factor of 0.38𝑚3/ℎis obtained. Considering that the selected solenoid valve has a 𝑘𝑣 of 0.09 𝑚3/ℎ it is clearly undersized. Which was not so evident due to the lack of technical data for the regulator and stop valve, it also emerges that the system is also constricted by the latter. This is proved by comparing the time constant with the burn time obtained considering a system flow factor of 0.38𝑚3/ℎ. The only way to correct this problem would be a complete redesign of the propulsion system, the solenoid valve, the polyurethane tubing, the stop valve and regulator, and since the last two item screw directly into the tank, a different tank option would be needed. Additionally, a new system of refilling would have to be implemented. Unfortunately 3 Design and Construction 49 6: The drawings of these CAD models can be found in the Drawings document section D.2 I Because of the low thrust obtained from the propulsion system, the vectoring angle should be as large as possible in order to produce enough torque effect necessary for the stabilization. I Keep the design as simple as possible. A mechanical failure in the TVC would result in the loss of control over the vehicle. It must be reliable. Once these requirements have been taken into consideration the design process begins by analyzing multiple TVC designs for solid fuel motors developed by the hobby rocketry world. With a general idea on how to proceed, a sketch is developed and then modelled in SolidWorks. After many tweaks of the geometric parameters, tolerances and the FDM parameters the following design is realized. Figure 3.19: Thrust vector control mechanism design. 1) Y-axis servo mount; 2) Inner gimbal; 3) External gimbal; 4) Engine mount; 5) X-axis servo mount. The design 6 is composed of a engine mount which can rotate about the vehicles x-axis, an inner gimbal that holds the servomotor controlling the movement in the x-axis, and a fixed external gimbal that holds the inner gimbal in place and allows the inner gimbal to rotate about the yaxis. The external gimbal includes a servo mount for the servomotor that controls the inner gimbal movement. Note that the vehicle coordinate system is determined by the IMU. Multiple iterations were performed and manufactured, starting with smaller wall widths in order to reduce weight. These were tested for strength and as a result thicker walls were deemed necessary. The design permits at least 15 º of movement in each axis. The result is an engine mount that can rotate about both axis, allowing it to point in any direction within the spherical cap defined by the 15 º axis limit. 3 Design and Construction 50 As for the connections, initially the idea was to implement ball bearings but after some consideration, simply connecting the gimbals together with screws would allow for rotation without the need for an axle. The screws serve as a kind of semi-axle. Naturally, the rotational friction is greater with this method, but the servomotors have enough torque to overcome this friction. The screws can be seen in Figure 3.19. Eventually this design is integrated to the vehicle’s base, which serves also as the landing gear mount and holds the outer and inner structure in place. The following figure illustrates the fabricated TVC mechanism integrated to the vehicle’s base. Figure 3.20: FDM fabricated TVC mechanism integrated to the vehicle’s base Taking a closer look at the servo, one can appreciate how the servo transmits movement to the engine mount via a strut. 3.3 Aerobrakes The aerobrakes serve a dual purpose. Firstly contributing to the vehicle’s stability and secondly helping with deceleration in order to reduce the amount of required thrust for vertical landing. This section details how they were sized and how the mounting design was created. As done for the other systems, the first step in the design process is to determine a list of requirements that must be considered: I As a result of the poor thrust results, the aerobrake surface area should be maximized in order to produce high amounts of drag with the purpose of decelerating. I Although the scope of the project only focuses on the landing aspects, in practice the vehicle would also be performing launch. When launching, drag has to be minimized by keeping the body profile to a minimum. This engenders a new design requirement: 3 Design and Construction 51 7: Drag isn’t a static load since it varies in time due to the acceleration of the vehicle. Having said that, since the increase in drag is gradual, when performing structural simulations it can be considered as a static load. Design Requirement 3.1 Aerobrakes must be retractable I The aerobrakes must be able to withstand both the static loads related to drag 7 and the dynamic loads related to the deployment. Once these requirements have been detected, the design process continues with a modification to the required thrust algorithm in order to obtain a better understanding of the relation of the vehicle’s drag to touchdown velocity with respect to its drag. The following figure exposes the findings: 00.050.1 0.15 0.20.250.3 0.35 0.40.450.5 CDA [m2] 4 6 8 10 12 14 16 18 Impact velocity [m/s] Impact velocity - drag relation Figure 3.21: Impact velocity - 𝐶𝐷𝐴 relation It’s worth considering that the impact velocity is related to the product of the drag coefficient and reference surface area. The reason for this is because the drag is not only created by the aerobrakes, but also by the vehicle’s body and the interaction between the two; and determining a reference area of the set is not straightforward. Having said that, the 𝐶𝐷𝐴 product serves the same purpose. As can be seen in the plot, naturally the higher the product’s value, the lower the impact speed. Consequently, obtaining high values of the product will be of interest. When it comes to shape and size, as a means of keeping the vehicle’s profile as low as possible when having the aerobrakes retracted, it is decided that the aerobrakes should be composed of 4 sections of tube of similar diameter to that of the body’s. As a result, when retracted, the aerobrakes are mounted radially in a concentric fashion, keeping the profile as small as possible. As for the surface area, the width of the aerobrake is determined by the tube diameter, which in is 80mm; and the length is maximized for greater surface area but limited in a way that it won’t interfere with the retracted landing legs, which turns out to be a length of 300mm. 3.3.1 CFD Simulation Once the aerobrakes have been sized, a CFD simulation is run using Solidworks’s Flow Simulation in order to determine the drag coefficient 3 Design and Construction 52 of a single aerobrake, which shall be needed for the structural simulation verification. To carry this out, a CAD model of the aerobrake is designed and a mesh is created. Three simulations at 5, 10 and 15m/s are run in order to determine the drag generated at each speed. Figure 3.22: Cut plot of the aerobrake model mesh. The simulation parameters are set as follows: I Incompressible flow. The vehicle’s velocity will never surpass the 0.3 Mach speed at which point the flow starts to behave subsonically and can’t be considered incompressible [13] [13]: Anderson (1991), Fundamentals of Aerodynamics (Mcgraw-Hill Series in Aeronautical and Aerospace Engineering) . IISA (International Standard Atmosphere) Sea Level conditions. IViscous flow. I Surface roughness of 34 𝜇𝑚 , a typical value for FDM 3D printing at a layer height of 0.20mm [22] [22]: Hartcher-O’Brien et al. (2019), ‘Surface roughness of 3D printed materials: Comparing physical measurements and human perception’ , which is the layer height used throughout the project. The following figure presents the results of the simulation performed with an incidence speed of 10m/s: Figure 3.23: Aerobrake CFD simulation with an airspeed of 10m/s. The black lines represent streamlines and the colors denote the velocity contours. a) Front view; b) Side view The simulations were setup in order to output the force generated in the direction of the Y-axis, which happens to be the drag force. Introducing the calculated drag values, the reference area into the drag equation 2.2, 3 Design and Construction 53 8: The vehicle’s body is a 80.00mm cardboard tube the mean value of the drag coefficient can be determined and results to be 𝐶𝐷=1.77 . Knowing that the thrust produced by the propulsion system was insufficient, it called for finding ways to increase the total drag produced by the vehicle. This is where aerobrakes with holes come in. The hypothesis is that by tapping wholes into the aerobrakes, flow disruption could be increased and as a consequence the the turbulent wake would be enlarged with the objective of increasing pressure drag. In order to test this hypothesis, a modified aerobrake model with 6mm diameter holes is designed, meshed and introduced into the flow simulation. Figure 3.24: Aerobrake with holes CFD simulation comparison. Airspeed: 10m/s. The black lines represent streamlines and the colors denote pressure contours. a) Aerobrake without holes; b) Aerobrake with holes. The 𝐶𝐷 of the aerobrakes is calculated in the same manner as the aerobrake without holes. its value is determined to be 𝐶𝐷=1.23 . This can be explained by observing the streamlines and pressure contours in Figure 3.24. The streamlines of the aerobrake with holes seem to show a more chaotic and disrupted turbulent wake, whilst the aerobrake with no holes shows a more streamlined wake. Having said that, the key is in the pressure difference above and below the aerobrakes. The aerobrake with no holes presents a bigger pressure differential of 137.22Pa, whilst the aerobrake with holes only has a 90.00Pa pressure differential. This demonstrates that the aerobrake with no holes has more pressure drag than its counterpart and therefore the aerobrake with holes is disregarded. Once the aerobrake design has been selected, a CAD model of it integrated with the vehicle’s body 8 is made with the purpose of running flow simulations in order to determine the vehicle’s 𝐶𝐷𝐴 coefficient. The body length of 500.00mm used is an estimation based on the inner components that the vehicle must house. 3 Design and Construction 54 Figure 3.25: Body and aerobrakes CFD simulation. Airspeed: 10m/s. The black lines represent streamlines and the colors denote velocity contours. Using the same method employed with the aerobrakes the drag coefficient - reference area product is determined to be 𝐶𝐷𝐴=0.13𝑚2 . With this result, Figure 3.21 can be used to estimate the impact velocity. However, note that the figure was developed considering a constant thrust of 2N and a drop height of 15m so results may vary from those obtained experimentally. The impact velocity is estimated to be 𝑉𝑖𝑚𝑝 =9.72𝑚/𝑠. 3.3.2 Aerobrake Mount Design Once the 𝐶𝐷 of the aerobrakes has been determined the mount design can commence. The process consisted of first sketching an idea and later designing a CAD model, fabrication with FDM, followed by tweaking with multiple iterations and finally a flight test to validate the design. Figure 3.26: Render of the aerobrake and mount assembly. 1) M3x20 slotted bolt; 2) Aerobrake holder; 3) Aerobrake - body mount; 4) Aerobrake fin 3 Design and Construction 55 The design consists of 2 main parts. The first is the aerobrake fin holder which serves the purpose of securing the aerobrake to the mount. its curved slot gives more rigidity to the fin in a similar way that pizza can stay straight if its crust is bent. The 4 holders are attached to the second part, the body mount. The attachments are done via joints that allow the rotation of the aerobrakes from a folded position to a deployed position, perpendicular to the vehicle’s outer wall. The screws attached to the holders serve as an anchor point for springs that will give the aerobrakes their controlled retractability and deployment aspect. In order to validate the design, first a load simulation is performed with Solidworks and secondly a flight test. In order to setup the simulation, the drag force has to be determined. This was achieved using the 𝐶𝐷 value calculated in the last section. For the integration of a safety margin, the maximum airspeed is considered to be 15m/s instead of 10m/s (the estimated airspeed). At this airspeed each aerobrake experiences 4N of drag force. The simulation is setup as with the following parameters: I Materials: The material used for the FDM 3D printing is PLA (Polylactic acid), and as for the aerobrakes, it was decided to go with the same cardboard tube the body is built from. The material properties of PLA were found online [23][23]: UL (2015), Polylactic Acid (PLA) Typical Properties | UL Prospector and introduced to the program. With respect to the type of cardboard, MDF (Medium Denisty Fiberboard) [24] [24]: MakeItFrom (2020), Medium Density Fiberboard (MDF) :: MakeItFrom.com is used as it is considered to be the most similar to the type of cardboard used. I Static simulation: Although the load varies in time due to the acceleration of the vehicle, the rate at which it does so allows for the study to be considered static. I Load: The load is considered to be a distributed force of 4N applied to each aerobrake. The following figures show the results of the simulation obtained after the assembly was meshed and the parameters prepared: Figure 3.27: Aerobrake static load simulation: Strain plot [ 𝑁/𝑚2 ] using the von Misses yield criterion. 3 Design and Construction 56 Figure 3.29: Phase 4 of the PP corrugated sheet thermoforming process Figure 3.28: Aerobrake static load simulation: Displacement plot [mm]. Deformation scale: 10. As can be seen in the plots, the maximum stress is located at the joint axle with a value of 25.21MPa. As for the maximum deformation, it is produced at the tip of the aerobrakes and has a value of 4.17mm. A FOS (Factor of Safety) plot is also generated, from which the minimum FOS of the whole design has a value of 5.90. Such a high value gives great confidence in the design’s capability for not collapsing under the load. When constructing the aerobrakes, it was realized that using cardboard was an issue due to its mass. Each aerobrake came in at 59.00g, meaning 236.00g for the set of 4. This wasn’t a good option considering that reducing weight is of utmost priority. Additionally, such a high fin weight caused for the joints to snap when the fins reached the full extent of the deployed position (limiter) due to the gained inertia. For these reasons the material was switched to the much lighter PP (Polypropylene) corrugated sheet. The advantage of this material is that for such a low sheet density, good bending moment resistance is achieved in the flute direction (direction of the corrugated lines). In order to gain the required curvature, the sheets are submitted to a home-made thermoforming process using a kitchen oven and a mould created from the same tube used for the vehicle’s body. The process consists of 5 phases9 9: Thermoforming design phases: IPhase 1: Heat oven to 180 degrees. Any higher and the sheets get too malleable and start to shrink. IPhase 2: Put the flat shape on the bottom half of the mould and leave in the oven for 2 minutes in order to preheat. IPhase 3: Remove the malleable sheet from the oven and then use the top part of the mould to evenly compress the form into the required shape. Add clamps to secure. IPhase 4: Place in the oven again for an additional 2 minutes. IPhase 5: Remove from the oven and allow to fully cool down before removing the clamps. . The result is an aerobrake fin with the same curvature as the main fuselage and a weight of only 15.00g. This translates into a reduction of 176.00g for the complete set. The load simulation was performed considering MDF as the material for the aerobrake fins, so in order to validate the design with this material, an experimental load test is performed by placing a mass of 0.40kg (4N) on at the center of the aerobrake, where its 𝐶𝑃 is located. The design passed the test, but regardless it is unknown how the design will react to the dynamic loads, especially now that the FOS is unknown. For this reason a flight test is carried out. The design successfully passed the flight test, performing as intended and without taking any damage. More on this flight test will be developed in Section 5.1 (Dummy Drop Test) on page 82. Ultimately, the design using corrugated PP is validated. 3 Design and Construction 57 Figure 3.30: Constructed aerobrake assembly. Left: deployed position; Right: folded position 10: 𝐾𝐸=1 2𝑚𝑉2(3.9) 11: Touchdown velocities that model rocket parachutes are designed to achieve. On the top part of the figure on the right the retracting springs can be seen attached to the M3x20 bolt. Below it in red is the deploying apparatus, which will be explained in section Section 3.5.1 (Quick Release) on page 63. Drawings of all the 3 components of the aerobrakes and its assembly can be found in the Drawings document section D.1. 3.4 Retractable Landing Legs This section details the design process of the retractable landing legs, a process consisting in the following steps: initial idea sketch, CAD modelling, structural simulation verification, fabrication, drop test, and finally re-iteration correcting the weak points. As carried out for the other subsystems, before starting the first step of the design process, a series of requirements are defined: I Adhering to design requirement 2.2, the legs must be retractable. I The landing legs must provide at least 41.50mm of clearance for the nozzle. I With the lack of sufficient thrust, the touchdown velocity is estimated to be 10m/s. At this speed and considering the expected weight of 1.5kg, the landing legs would have to absorb 75.00J of kinetic energy 10 . This is going to be a difficult task to achieve considering the weight and size restrictions and also the deployability aspect. In conclusion, these conditions are unrealistic and ideally the velocity would need to be almost null at touchdown or at the most in between 3.00 and 4.50m/s 11 . So, even though the landing legs are going to be designed for a impact velocity of 10m/s, if the design were to fail under these conditions it wouldn’t be considered a failure. With the subsystem requirements identified the next steps of the design process can be carried out. A CAD model is created from a design sketch, below is the result of the final iteration: 3 Design and Construction 58 Figure 3.31: Render of CAD landing leg assembly in the deployed configuration. 1) Vehicle base; 2) M3 bolts; 3) Leg rotation axles; 4) Struts; 5) Strut latches; 6) Landing legs. Retracting springs are fitted in between points 2 and 3. The design is composed of three main parts or sets of parts (axisymmetry). The first is the vehicle base, which is the same component that the TVC mechanism is fixed to. It also has the landing leg hinges which house the axles that join the landing legs to the base. The landing legs are designed to be fixed at such an angle that permits a certain degree of flexibility in order to help absorb the impact energy. Also, they are designed so that the contact points are optimally distanced from the vehicle’s center of mass with the objective of increasing ground stability and minimizing the likelihood of toppling over if the vehicle were to touchdown with some vertical misalignment. The final parts are the struts, which serve the purpose of deploying the landing legs and retaining them in their deployed position. For that aspect, the struts are connected to the the vehicle’s base axles with extension springs in a way that, if not impeded, the struts push the landing legs down, where they are locked into position with a latch that catches the strut once it reaches the deployed position. When deployed, the landing legs give a clearance of 66.67mm, enough to provide protection to the nozzle. 3.4.1 Structural Simulation With the means of verifying the design a series of structural simulations are carried out with Solidworks. The simulations are dynamic drop test simulations where the model is given an impact velocity of 10m/s and the mass is overridden to 1.25kg. The results of the simulation are multiple plots representing steps spanning 280 𝜇𝑠 after impact, these are submitted to a Von Misses stress analysis in order to determine the maximum stress values the model is exposed to. In total two of these simulations are carried out, the first for the initial design and the second for a reiterated more, robust design, that is improved by analyzing the results of a real life drop test performed on the first iteration. The following figure shows the results of the simulation of the first design iteration: 3 Design and Construction 65 Figure 3.39: Aerobrake deployment Figure 3.40: Landing legs deployment Subsystem Event Frames Time [ms] Aerobrakes Rubber band snap 57 238.00 Full deployment* 112 466.00 Landing legs Rubber band snap 49 204.00 Full deployment* 60 250.00 Table 3.9: Deployment delays calculated from 240fps footage. *Total time from triggering to full deployment. 3 Design and Construction 66 Figure 3.41: Internal structure strut - disk design. Figure 3.42: Mesh of the holder base model. The purple arrows represent the load whilst the green arrows represent the fixation points. 3.6 Structure The structure refers to the vehicle’s body and the internal parts that hold all the components and subsystems in place. This section will describe how these two tasks are developed as well as detailing 3D printing parameters considered throughout the project and finally the mass and the dimensions. When it comes to the vehicle’s body, a 2mm thick 80mm cardboard tube is selected because it provides enough rigidity for a reasonably low weight trade off. A common practice to increase the tube’s strength is to cover it in a diluted epoxy solution, however this wasn’t carried out because it would increase the weight and the additional strength was deemed unnecessary, considering that for a working propulsion system the impact velocity would be low. As can bee seen in figures to come, two cutouts outs are made in order to access the tank refilling nipple and the stop-valve. The top of the tube is left uncovered for access to the battery back and the Arduino. As for the internal structure, it was required to find a way to attach all the components inside the body at specific heights. The solution was a modular and adjustable strut - holder disk system, where three wooden struts are fixed co-axially to the vehicle’s base. Then a series of disks that slot on to the struts are designed and personalized for each component. The disks are fixed using M3 bolts that dig into the wood, meaning that the height can be adjusted at any time. This proved to be very useful to find ideal height placement for each component. Figure 3.41 clearly shows this system where the holding disks are slotted through the wooden struts. 3.6.1 Topology Optimization The design of the disks was seen as an opportunity to find a way of reducing weight without compromising functionality. For that a topology optimization study on Solidworks is performed on the base model of the disk. Basically, topology optimization is a mathematical method that optimizes material layout within a defined mesh for a given set of loads, boundary conditions and constraints. The first step is to design the base model and then mesh it. Then, it’s necessary to specify the loads (10N) and their point of application (inner wall), the fixation points (strut holes) and the material (PLA). Once the mesh has been created and the conditions set, a study goal of reducing the mass by 60% by removing the parts of the mesh that least contribute to the model’s strength is set. The process iterates until converging on the mass reduction goal. The results are shown in Figure 3.43 on the next page 3 Design and Construction 67 Figure 3.43: Topology optimization study results. Left: Meshed model with removed material. Right: Smoothed out version The resulting model is only 40% of the mass of the original. Considering that 5 disks are used, this process allowed for a saving of 67.5g. Although this value is small compared to the total mass of the vehicle, every little bit helps. Once the optimized disk design is obtained, it is modified to fit different components: one for supporting the solenoid valve, two for holding the tank in place, one for the electronic circuit, Arduino and batteries and finally one for the IMU module. This last one was designed to fix the IMU in place aligning the module’s axis with the TVC mechanism axis. By doing so the vehicle’s system of reference is defined. The following figure shows the modified base disk for retaining the solenoid valve. Figure 3.44: Solenoid valve holding disk 3.6.2 FDM Parameters Fused deposition modelling is the type of 3D manufacturing used to make many of the vehicle’s parts. When it came to printing out the parts a few aspects were considered: ILayering direction: FDM consists of layering lines of melted PLA filament on top of each other. A consequence of this manufactur- 3 Design and Construction 68 ing process is that the prints are anisotropic, meaning that they have different mechanical properties in different directions. For example, the prints are less resistant to traction in the layering direction. This basically required for the model do be positioned in a certain way with the means of favouring the strength for each case. IInfill geometry and density: In many cases when manufacturing parts by FDM the model is not completely solid, but rather its composed of a combination of walls and an infill geometry. The density of the infill can be changed, keeping in mind that there is a direct relation with weight and strength. Also the geometry of the infill can be changed. Different geometries are selected depending on what anisotropic strength qualities are needed. A geometry that has been used quite a lot is the gyroid geometry since it is the infill that is most isotropic. However, in order for the nozzles to withstand the high pressures of the propulsion system, their infills were set at 100%. The following table specifies the 3D printing parameters used throughout the project: Parameter Value Layer height [mm] 0.20 Wall thickness [mm] 0.80 Printing temp. [ºC] 215.00 Build plate temp. [ºC] 50.00 Initial layer build plate temp. [ºC] 60.00 Print speed [mm/s] 50.00 Table 3.10: 3D printing parameters. 3.6.3 Mass and Dimensions The following table recollects mass parameters. A more complete mass breakdown can be found in Annex C. Note that the wet mass is slightly Parameter Value Wet mass [kg] 1.61 Dry mass [kg] 1.56 Propellant mass [kg] 0.050 𝑍𝐶𝑂𝐺* [cm] 29.90 Table 3.11: Mass and balance parameters. *Center of mass position from the vehicle’s base for deployed aerobrakes. higher than the estimated value of 1.5kg. For future iterations this value should be decreased by redesigning parts, but for the current iteration it is considered valid. As for the overall dimensions, a detailed assembly drawing can be found in the Drawings document section D.7 including the internal disk heights. Parameter Value Aerobrake wingspan [mm] 755.00 Total height [mm] 587.00 Body diameter [mm] 80.00 Table 3.12: Overall dimensions of the vehicle. 3 Design and Construction 69 Figure 3.45: Constructed vehicle. Left: External view with deployed aerobrakes; Right: Internal view. Software Development 4 4.1 PID Controller . . . . . . . 70 4.2 Closed Loop System Simulation ................ 71 4.3 PID Tuning . . . . . . . . . 73 4.4 Program . . . . . . . . . . . . 77 This chapter explains how the stabilizing algorithm using a closed loop control system simulation is developed and how it is implemented as a program into the flight computer. Aspects surrounding the program such as running sequence and optimization will also be exposed. First of all the PID controller is defined explaining what purpose it serves for the stabilization algorithm. 4.1 PID Controller A PID controller is a device used to control a certain process variable by employing closed loop feedback[26] [26]: Electronics \ Project \ Focus (2019), PID Controller : Working, Types, Advantages & Its Applications . The term PID stands for Proportional Integral Derivative, and each one of these is a control term with it’s own functionality. Figure 4.1: Block diagram of a PID controller in a feedback control loop system. 𝑟(𝑡) is the setpoint (SP), 𝑒(𝑡) the error, 𝑢(𝑡) the PID control variable, 𝑦(𝑡) the process variable (PV) and "planta" the process block. PID controller overview by Arturo Urquizo is licensed under CC BY-SA 3.0 [27] The PID inputs the SP-PV error 𝑒(𝑡) and outputs a control variable 𝑢(𝑡)which is the result of a weighted sum of the control terms: 𝑢(𝑡)=𝐾𝑝𝑒(𝑡) + 𝐾𝑖∫𝑡 0 𝑒(𝑡) + 𝐾𝑑 𝑑𝑒(𝑡) 𝑑𝑡 (4.1) where 𝐾𝑝 , 𝐾𝑖 and 𝐾𝑑 are control term coefficients. Even though the PID controller has three terms, it is possible to use only one or two terms to provide adequate control. In this case all that needs to be done to "deactivate" a term is set it’s coefficient to 0. All combinations of P, I and D are possible. As mentioned above, each control term influences the controller output in a different way: IProportional term (P): gives an output proportional to the error e(t), comparing the desired SP with the feedback process variable. If the error is 0, so will the proportional gain. In other words, if used alone, the P term requires error to operate. In this 4 Software Development 71 Figure 4.2: Vehicle MMOI determination. case the proportional term will output the TVC angles proportional to the vehicle’s inclination. IIntegral term (I): integrates the error over a period of time until the error reaches 0. This solves the issue with only using the P term where an error is needed. For this case the integral term is useful in order to compensate for TVC misalignments. IDerivative term (D): this term derives the error over a period of time, giving it the ability to predict the future behaviour of the error. In this case the derivative term will be determining the inclination angular velocity and acting accordingly. The process variable 𝑦(𝑡) outputted from a closed loop system is characterised by parameters such as overshoot, rise time, settling time, gain and phase margins... but for this case the parameters of most relevance are: 1. Rise time: The time that it takes the process variable 𝑦(𝑡) to go from 10% to 90% of the SP. 2. Settling time: The time time that it takes the process variable 𝑦(𝑡)to settle within a 5% margin of the SP. Due to the short flight time it will be of most importance to reduce these values with correct PID tuning. 4.2 Closed Loop System Simulation The stabilization algorithm is developed using Matlab Simulink, a graphical programming environment for simulating and analyzing dynamic systems. First of all it is necessary to determine the vehicle’s MMOI (Mass Moment of Inertia) to describe how it will respond to the thrust. In order to do so the vehicle is hung horizontally from two strings attached to the vehicle equidistantly from it’s center of mass. In this configuration the MMOI can be calculated as such [28] [28]: Barnard (2020), Modeling a Thrust Vectored Rocket In Simulink : 𝑀𝑀𝑂𝐼 =𝑚·𝑔·𝑇2·𝑑2 4𝜋2𝐿(4.2) where 𝑚 is the vehicle’s mass [kg], 𝑇 the oscillation period about the COM [s], 𝑑 the distance from the attachment points to the COM [m] and 𝐿 the suspension height [m]. In pursuance of the period, the vehicle is tilted about it’s COM and then timed for the completion of 10 full oscillations. As a result, the inertia is calculated to be 𝑀𝑀𝑂𝐼 =0.062𝑘𝑔𝑚2 Once this value has been determined the closed loop system drop simulation can be designed. Figure 4.3 and shows the block diagram representing the closed loop system. It’s worth mentioning that as a result of the vehicle’s axial symmetry, the simulation is simplified to a 3-DOF system since the vehicle should behave the same in all axis. The adhering list describes the different blocks of the simulation. 4 Software Development 72 Figure 4.3: Simulink closed loop drop simulation. 1. The thrust is inputted to the system directly from the plot from Figure 3.18. For PID calibrating purposes, the thrust can be overridden to a constant value. 2. The thrust is decomposed into x and z components according to the TVC angle. 3. The x component of the thrust is multiplied by the moment arm (distance from TVC to COM) in order to obtain the stabilizing torque. 4. The drag is calculated according to the current velocity and yangle (vehicle’s angle with respect to the vertical) is added to the z thrust component. 5. The 3-DOF block is setup with the vehicle’s mass, initial height (15m) and MMOI. It takes the decomposed forces and torque as inputs and outputs the y-angle, height and speed. 6. The y-angle is converted to degrees and sent to the PID. 7. The 𝑢(𝑡) PID control variable is calculated. The PID’s time domain is setup as discrete-time coinciding with the refresh rate 4 Software Development 73 of the flight computer which has a value of 1390 𝜇𝑠 (determined experimentally, more on the topic in Section 4.4.3). This output is limited to 15 º due to the mechanical limitations of the TVC design. 8. A transport delay corresponding to the delay in between sending a signal to the servos and the moment they reach the required position. Naturally this delay is dependent on the magnitude of angle change, but for simplification purposes a mean value of 150ms is used. This value is determined experimentally with the use of slow-motion footage of know frame rate. 9. The system error 𝑒(𝑡) is determined from subtracting 𝑢(𝑡) from the system’s setpoint SP which is 0 º , considering that the aim is to keep the vehicle vertical. The angle error 𝑒(𝑡) closes the loop by decomposing the thrust input (1). 10. The system outputs the setpoint, the error and the y-angle. The following figure shows the height of the vehicle as a function of time for a wet mass of 1.61kg. The touchdown time of 2.10s is very similar to the value of 2.04s predicted in the Required thrust algorithm Section 2.3.2 (Required Thrust Algorithm), a difference of approximately 3%. This gives confidence in the validity of both the algorithm and the simulation. Figure 4.4: Closed loop simulation flight trajectory. Time is in seconds. 4.3 PID Tuning In order for the PID to properly respond to the closed loop feedback it has to be calibrated. There are multiple ways of going about this and one of the most common is the Ziegler-Nichols method [29] [29]: Ziegler et al. (1995), ‘Optimum settings for automatic controllers’ . This heuristic method begins by first setting the proportional, derivative and integral gains to zero in front of a unity step input (the initial angle of the vehicle is set to 1º). Then the proportional gain is incremented until it reaches the ultimate gain 𝐾𝑢 at which point the output has stable oscillations of constant period and amplitude. Once this value is 4 Software Development 74 achieved other parameters are calculated from which the three gains can be determined. Unfortunately this method did not work for the simulated system because the ultimate gain could not be found with precision because the 𝐾𝑝 gain nearing 𝐾𝑢 had values of the order of magnitude of -2 (0.01), making it very sensitive and therefore extremely difficult to find 𝐾𝑢 . The reason behind this is believed to be the servomotor transfer delay (block 8 of Figure 4.3). As an alternative the inbuilt Simulink tuner is used. This app tunes the PID according to the closed loop’s transfer function. Once the application has determined the gains they are tweaked using manual tuning, where the gains are modified independently to achieve the smallest rise and settling times possible. The following table shows the effect of increasing a certain gain independently. Table 4.1: Effect of increasing a certain gain independently. Extracted from [30]. Parameter Rise time Overshoot Settling time Steady-state error Stability 𝐾𝑝Decrease Increase Small change Decrease Degrade 𝐾𝑖Decrease Increase Increase Eliminate Degrade 𝐾𝑑Minor change Decrease Decrease No effect in theory Improve if 𝐾𝑑small Figure 4.5 shows the results obtained with this method. Figure 4.5: Closed loop simulation output for 2N of thrust and a servo delay of 150ms. Gain Value Parameter Value 𝐾𝑝0.24 Step input [º] 1.00 𝐾𝑖0.00 Rise time [s] 2.68 𝐾𝑑0.34 Settling time [s] 3.64 Table 4.2: Closed loop system parameters. 2N thrust and 150ms servo delay. As can be seen, the vehicle’s inclination with respect to the vertical (y-angle) starts off at 1 º and after about 7 seconds it reaches the SP of 0 º . Something that might catch attention is that the integral gain is set to zero. This is done because for an unknown reason the integral term worsens the settling time and introduces a constant error. To solve this 4 Software Development 81 4.4.3 Code Optimization The main part of the code is the loop (4 last blocks from Figure 4.9). The functions therein take time to complete. With the means of calculating the cycle rate, the code is modified to count how long it takes to execute 10,000 cycles and then the mean value is determined to be 4052 𝜇𝑠 per cycle. This happens to be 518 cycles for a 15m drop. The idea is to reduce this time and increment the number of cycles the vehicle can perform during it’s flight with the objective of increasing the PID’s responsiveness. In order to do so the same operations is performed but with each function independently: Function [𝜇𝑠/𝑐𝑦𝑐𝑙𝑒] IMU refresh 930 PID control variable 85 Servo refresh 144 LiDAR refresh 2893 Total 4052 Table 4.7: Loop function execution times. The previous table shows that communicating with the LiDAR module is the process that requires most time. It emerges that the height doesn’t need to be updated every loop so the code is modified for it to update every 20 loops. With this modification the loop cycle rate drops to 1390𝜇𝑠/𝑐𝑦𝑐𝑙𝑒 . This equates to 1511 cycles for a drop of 15m, almost three times the previous value. This is a great improvement and even though the refresh rate of the LiDAR is reduced significantly, it still refreshes every 20cm which is enough for the current conditions, since the only operation to complete is to trigger the release of the landing legs at a height of 5m. Validation and Results 5 5.1 Dummy Drop Test . . . . 82 5.2 Static Stabilization Tests85 5.3 Next Steps . . . . . . . . . . 86 This chapter records and analyzes the tests carried out with the prototype models; a dummy drop test and static stabilization tests. Additionally it sets out the steps that should be considered if vehicle were to be re-iterated. 5.1 Dummy Drop Test This test is performed to assess how the aerobrakes and landing legs behave and for examining the flight mechanics without risking the destruction of the precious internal components. In order to do so an exact replica is fabricated and filled with golf balls in order to simulate the wet mass for the complete vehicle. Note that this method does not guarantee that the dummy will have the same MMOI as the final vehicle, but for the purposes of this experiment this is not relevant since there will be no active stabilization. The test is performed from a 15m tall building with an interior patio that serves as the landing zone. It is worth mentioning that the drop height is not the required 20m calculated in previous sections, but then again, for the purpose of this experiment where there is no thrust, the height does not have to be exact. The test is filmed with 240 and 480fps footage which will allow closer examination of the behaviour of the aerobrakes, the stability and the landing legs. It is worth mentioning that the drop is performed manually and some angular velocity is purposely given in order to see whether the vehicle is stable or not. The aerobrakes initially are retracted in order to see how they deploy. Unfortunately the same cannot be said for the landing legs because since the dummy has no electronics, there is no way of triggering the deployment mid-flight. Ergo the legs will be deployed for the entirety of the flight. The predictions made before the test are: 1. The vehicle impact speed should be around 9.72𝑚/𝑠. 2. The landing legs are not likely to withstand an impact at such a great speed. 3. Having such big aerobrakes means it’s very probable that the vehicle’s CP is located above it’s COM, meaning it should be stable. 4. According to the flow and structural simulations, the aerobrakes should not fail. The following figure shows stills from the 240fps footage which records the flight of the vehicle. 5 Validation and Results 83 Figure 5.1: Dummy drop test 240fps footage The flight duration was 1.86s, a bit lower then the predicted 2.1s (Section 4.2). This is because there could be a variation in between the simulated drag coefficient and it’s real value, but most like it is due to the fact that the exact height of the building is unknown. 15m is an estimation by counting floors. Having said that, this does not affect the validity of the test. As seen in the figure, the aerobrakes successfully deployed without sustaining any damage whatsoever. This result validates the aerobrake design and the use of corrugated PP as a material choice for saving weight. Also, one can observe throughout the still images that the vehicle has restoring torque: the vehicle starts tilted to the left and then corrects itself to the right, and back again to the left just before impact. This validates design requirement 2.1, where the CP must be located above the COM in order to achieve stabilizing thrust. In other words, the vehicle passively stabilizes itself without the need of thrust, reducing the amount of thrust needed for stabilization. It may not be visible in the figure but the vehicle rolled a little bit, specifically it performed one and a quarter revolutions about it’s zaxis. This shouldn’t be a problem because the IMU and TVC axis are always coupled regardless of the roll angle and are in the same frame of reference. Using the slow-motion footage and a known distance in the frame, the impact velocity is calculated to be 9 . 71 𝑚/𝑠 which is amazingly exact to the value predicted. The following figure shows how the landing legs behave at such a impact speed. 5 Validation and Results 84 Figure 5.2: Dummy drop test 480fps footage The figure clearly shows that the landing legs are not capable of tolerating such impact speeds. We also observe the support struts slipping off their latches. This is one of the aspects that was improved with the second iteration of the landing leg design. Also, the vehicle initially contacts with only one leg. This obviously is no the intended working condition of the leg so it should perform better if active stabilization is executed and the vehicle touches down vertically on all for legs at the same time. Observing the damage that the legs experienced from this test, the weak points of the design are identified (Figure 3.33) and improved upon on the second design iteration. Although seeing the destructiveness of this test, it is unlikely that the reiterated design would survive the test undamaged. Then again, these conditions aren’t ideal considering that if the propulsion system could output higher values of thrust, the touchdown speeds wouldn’t be so large. The bottom left image shows how the vehicle’s body absorbs the impact energy and deforms to a notable extent. This is alarming because if the propulsion system were to be on board, there would be a risk of the high pressure system taking damage and even exploding, a major safety concern. 5 Validation and Results 85 Figure 5.3: Static stabilization test rig. 5.2 Static Stabilization Tests In order to test the stabilizing algorithm and the PID tuning a series of tests are carried out. To so a the vehicle is hung from a cinema lighting fixture at the vehicle’s center of mass as shown in Figure 5.3. This configuration allows for the vehicle to tilt freely about it’s COM in the plane perpendicular to the ground. Additionally it allows for tilting in the plane parallel to the ground, but it can’t to so without the influence of the torque produced when the string holding the vehicle twists. Also, it’s worth mentioning that applying a 90 º offset to the IMU readings is necessary for compensating the horizontal position of this configuration. That said because of how the IMU works, when tilted the IMU is only capable of giving accurate tilt angle readings in the plane perpendicular to the floor. All of this means that this rig only allows for testing stabilization in one axis independently. Nevertheless, this is not an issue due to the fact that the vehicle is symmetrical and should behave in the same way for both axis. A major disadvantage of this test rig configuration is that due to small misalignment’s of the TVC mechanism cause for the vehicle to start to rotate about the direction perpendicular to the ground. This is inconvenient and adds difficulty to the examination of the stabilization behaviour. In retrospect, future iterations of the vehicle could do with a better deigned test rig that allows for the vehicle to be mounted vertically and allows for tilting in both axis simultaneously. To perform the tests, the vehicle’s HP tank is refilled and the different PID gains from Section 4.3 are applied. Whilst using the gains from Table 4.2, when a destabilizing force is applied, the vehicle corrects it’s tilt with large rising and settling times, as predicted by the simulation in Figure 4.5. A second test is performed using the the gains from Table 4.4. These gains were modified manually with the attempt to reduce rising and settling times. As a result, like the simulation predicted, the vehicle enters an unstable state, oscillating up and down. This test confirms that the the large servo delay limits the rise and settling time of the process variable (tilt angle). In hindsight, integrating a means of storing the PID control variable and IMU angles would be very helpful to get more detailed results. This could be done using an SD storage module. The data recorded could be compared to the simulation data and the PID could be tuned in a more precise way. Having said that, this option was not carried out because the tests carried out allowed for visual confirmation of the fact that the thrust isn’t great enough for faster rising and settling times and that the servo delay also plays an important role with these parameters. The results from these tests beget the decision to not carry out a flight test with final vehicle and all it’s components. Reason being that, a part from the fact that the test would be destructive and pose a safety risk due to possible damage to the HP propulsion system, the test is likely to not produce any new information. The dummy drop test has already validated the aerobrake design and proved that the legs are unlikely to withstand an impact of such velocity. On the other hand the stability tests show that the rise time is much greater than the 5 Validation and Results 86 flight time itself, meaning that the vehicle won’t be able to stabilize in time for impact. The only information new information that could be acquired is to see if the vehicle can decelerate and if the flight program works. As for the first aspect, having such low thrust will have little effect on deceleration, and as for the second aspect, the program and it’s functions were testes successfully in a controlled environment. 5.3 Next Steps It’s no secret that the aim of the project hasn’t been accomplished to it’s entirety. In great part this is due to the time and budget limitations. There are still many aspects that could be worked on in future iterations in order to reach the project’s goal. This section goes through what would be the next step one would take if the project were continued. Firstly and most obviously, the propulsion system would have to be redesigned from the bottom up in order to achieve the required thrust. When redesigning, the flow factor of the pneumatic system components has to be of utmost importance since it has the greatest impact on the thrust generated. Backed up by the results from the burn algorithm Section 2.3.3 (Burn Algorithm), it is still believed that air can be used as the propellant with properly sized components. Having said that other propellant options such as Nitrogen could be considered with a greater budget due to it’s higher 𝐼𝑠𝑝. Another key factor would be reducing the servo delay in order to obtain faster stabilization response times. This could be done by obtaining servomotors with faster angular speeds and by integrating a servo controller module to the electronic circuit, delegating processing power from the flight computer to the controller module. If the prior modifications are carried out successfully, a window of new areas of work would arise consisting in the following aspects: 1. Having sufficient thrust would allow for less robust landing legs and aerobrakes of smaller reference area. This opens the opportunity of reiterating these designs with the objective of reducing the vehicle’s wet mass. 2. Integration of a SD storage module to the flight computer in order to record the PID control variable, servo position angles and IMU tilt angles for more precise PID tuning. 3. The construction of an improved static stabilization test rig with the characteristics and benefits mentioned in the previous section. 4. Integrate thrust amount control using PWM to adapt to the thrust needs according to the height of the vehicle. This would also need to be controlled with a PID controller and integrated into the closed loop feedback system. 5. Multiple flight tests would need to be performed in order to tweak control gains and parameters. To carry this out in a non destructive way, a safety apparatus would need to be designed 5 Validation and Results 87 and constructed to catch the falling vehicle. 6. A final flight test without connection to the safety tether when confidence in the stabilization algorithm is gained. If these previous steps were realized, the project’s aim and objectives would be achieved. Budget 6 The cost to realize this project amounts in total to 13,635 € . This value can be broken down into engineering, material and energy costs. Item [€] Engineering costs 13,230.00 Material costs 375.00 Energy costs 30.00 Total 13,635.00 Table 6.1: Total cost of the project. For a more detailed cost breakdown refer to the attached budget document (Attachment E). As stated in detail in the introduction pages, this project has a scientific purpose and the final product is not intended to be commercialized. Therefore, no economic feasibility study has been carried out. Environmental Aspects 7 7.1 Energy Consumption Impact ................. 89 7.2 Materials . . . . . . . . . . . 89 This section carries out a brief environmental impact study. 7.1 Energy Consumption Impact As can be seen in the budget attachment in section E.3, the energy consumed for the elaboration of this project can be attributed to 3D printing and the use of a PC. Using the 3D printing software logs (Ultimaker Cura) the print time can be established to be approximately 180hs, which includes reprints and old iterations. The printer used for this project is the Creality Ender 3 which has a power consumption of 350W. Additionally, the PC usage is estimated to be 685hs, which includes the simulation running times. The computer used has an average consumption of 200W. With these consumption and usage values, the total amount of energy consumed for the elaboration of this project is estimated to be 200kWh. According to the European Environment Agency, Spain produced an average of 0.21kg of 𝐶𝑂2 for every kWh produced [31] [31]: Agency (2020), Greenhouse gas emission intensity of electricity generation — European Environment Agency . Additionally, for every kWh used there is 0.51mg of radioactive waste produced [32]. In conclusion, for the elaboration of this project 42kg of 𝐶𝑂2 and 102mg of radioactive waste is produced. 7.2 Materials Since the project is for proof of concept purposes, finding materials with low environmental impact wasn’t a priority. Having said that, if the aim could be achieved, the propellant used for the gas thruster is of zero emissions and it is environmental friendly. On another note, most of the components used for the project can be reused for future iterations or different projects altogether, extending the end of life period. Conclusions 8 This project set out to design and construct a scaled prototype of a reusable vertical landing vehicle with active stabilization and cold gas thrust capabilities. This main objective was not carried out to it’s entirety due to design constraints, time and budget limitations. Having said that, a lot of work has been done to lay down the foundations required for realizing this highly complex task. This section will analyze what requirements have been fulfilled and which have not due to the constraints stumbled upon along the way. The main design constraint with no doubt is the propulsion system. As seen in Section 3.1.2 (Nozzles, Tests and Troubleshooting), the minimum required thrust of 20N established in Section 2.3.2 (Required Thrust Algorithm) couldn’t be achieved due to the restricting flow factors of the pneumatic components that make up the system. Unfortunately, with the chosen approach of the paintball pneumatic components, no alternative parts with adequate flow factors were found. This means that the propulsion system needs to be designed from scratch. It is believed and backed up by the burn algorithm of Section 2.3.3 that air can be used as the propellant successfully if mass flow constrains could be avoided with proper professional pneumatic components. Not such a limiting constraint but important nonetheless is the servomotor delay. As determined in Section 4.3 (PID Tuning) and verified in Section 5.2 (Static Stabilization Tests) the current servomotor delay is so long that it constrains the TVC stabilization response time. Combing this with the fact that the thrust produced is only 10% of that required, active stabilization is carried but the stabilization response time too high for the flight time frame in order to make a significant difference. If the required thrust were to be achieved and delay were to be reduced to 20ms by selecting better servos or integrating a servo controller module, it has been proven in Section 4.3 that adequate stabilization response times can be achieved. Going forward, if the previous issues solved, a window of working areas would arise that haven’t been able to be addressed in the current iteration. These would include integration of thrust amount control, on board data storage and multiple flight tests in order to tweak and perfect the stabilization algorithm. For more details on these next steps, refer to Section 5.3 on page 86. Project requirements from Section 1.3 IREQ-001 : Vehicle shall be capable of decelerating using a cold gas thruster as a means of retro-propulsion. IREQ-002 : Vehicle shall be capable of active stabilization with the use of Thrust Vector Control. IREQ-003 : Vehicle shall be capable of sustaining hovering flight. IREQ-004 : Vehicle shall be capable of complete autonomous flight. IREQ-005 : Vehicle shall be reusable. IREQ-006 : Vehicle shall have a lightweight design. IREQ-007 : Vehicle shall have FDM manufactured parts for educational purposes. Having commented on the main design constraints, it’s time to take a look at the requirements identified at an initial stage of the project and see if they have been accomplished or not. Clearly REQ-001 is not achieved because the produced thrust is to low. Having said that, the vehicles does decelerate on account of the drag generated by the large deployable aerobrakes. As for REQ-002, it can be said that it has been accomplished but with a catch: the response time is too low for the project’s needs.