The Stratos Rocket Design, simulation and production of a record breaking rocket
J uly 2009 Mark Uitendaal
The Stratos Rocket Design, production and simulation of a record breaking rocket
By Mark Uitendaal B.Sc. Master of Science Thesis July 15 th , 2009
This thesis report embodies the thesis work for obtaining the Masters Degree of the study Aerospace Engineering at the Delft University of Technology. The examination committee iii consists of C.J.M. Verhoeven, B.A.C. Ambrosius, B.T.C. Zandbergen and B. Ouwehand.
I would like to thank especially my primary supervisor Chris Verhoeven for believing in the project in the most critical and stressful times. Above all, Chris granted me full freedom in the Preface way I materialized and structured this project, something I valued very much.
I have about 12 years of experience in the field of amateur rocketry doing a couple of “firsts” in rocketry in the Netherlands. A long desire of me was to launch a rocket at Esrange and to shatter the European Altitude record for amateur rockets. This was the reason why I started the Stratos project at DARE.
The Stratos project was the most challenging project I ever undertook up to now, and it is certainly the highlight of my study at Delft University of Technology. The fellowship within the group, the trip to Esrange and the actual launch of the rocket which broke the European Altitude record for amateur rockets are things I will never forget.
I would like to thank Leon Krancher, my companion in many rocket-projects before Stratos. Because of Leon the rocketry passion had a fertile soil to grow. I would also like to thank my parents for their continuing support in all endeavours, and my roommates of the Penthouse/CAVE II.
I would like to express my deepest gratitude to all the members of the DARE Stratos team: Arjan Fraters, Auke van der Valk, Bart Hertog, Bryan Tong-Minh, Christina Aas, Eric Smit, Frank Engelen, Hein Olthof, Jasper de Reus, John-John Boeva, Martijn de Milliano, Olga Motsyk, Peter van Gemert, Ragiel Wildvank and Robin F. Kearey. Not only the pure dedication during the work, but also the friendships along the whole project. Without this team of very dedicated people, this project could not have succeeded in the way it did. I sincerely thank you all for everything!
Delft, June 18th, 2009 Mark Uitendaal B.Sc.
. M.Sc. Thesis Mark Uitendaal B.Sc.
iv Preface
Mark Uitendaal B.Sc. M.Sc. Thesis
At the 17th of March 2009, a rocket called Stratos was launched, by Delft Aerospace Rocket Engineering, or DARE for short. The purpose of this rocket was to break the European v altitude record for amateur rockets which was at that time 10.7 km. The objective of this thesis is to give a detailed insight in the design, the simulation tools, the production process and the results of the mission. Abstract A design of a small sounding rocket, such as Stratos, is a good example of an interdisciplinary challenge. An optimal design is a combination of structures, manufacturability, propulsion, aerodynamics, electronics and many other factors. The design-philosophy as well as the detailed design of the Stratos rocket is explained.
Every rocket needs propulsion in order to lift of the ground. A solid rocket motor performance simulation tool, named MPPT was written in order to aid in the design of the solid rocket motors of the Stratos rocket. In order to evaluate different designs and to simulate different launch scenarios a separate flight simulation program was written. The flight simulation program, named FTPT can evaluate different rocket configurations.
The Stratos rocket was built and tested by DARE. This incorporates a detailed production planning. For the Stratos, which was entirely built by volunteers, a new production planning concept was tried. This production concept, named “burst-production” is going to be improved and used in the future by DARE.
The Stratos rocket achieved an apogee altitude of 12.551 meters at the Esrange Space Centre, thereby setting a new European altitude record for amateur rockets. A detailed flight trajectory reconstruction is done, whereby differences between simulation and reality are explained.
The design philosophy of the Stratos rocket, MPPT, the FTPT and the production planning concept are valuable tools in the development of newer and more powerful rockets, which could ultimately result in a successor of the Stratos rocket.
. M.Sc. Thesis Mark Uitendaal B.Sc.
vi Abstract
Mark Uitendaal B.Sc. M.Sc. Thesis
Preface iii Abstract v vii
Nomenclature xi
Introduction 1
1 Project objectives 3
2 Rocket design 3 ofContents Table 2.1 A brief introduction into rocket motion 2.2 Motor burnout 2.3 Rocket stabilization and flight 2.4 The rocket design 2.4.1 The booster stage: 2.4.2 The main stage: 2.4.2.1 The sustainer section 2.4.2.2 The capsule section 2.5 Recovery 2.5.1 Capsule separation and recovery 2.5.2 Parachute activation 2.6 The Pyrotechnics of the vehicle.
3 Propulsion design 37 3.1 Propulsion 3.2 Propulsion options and requirements 3.3 Booster motor design 3.3.1 Thrust profile 3.3.2 The design of the booster motor 3.4 The upper stage motor design 3.4.1 The thrust profile 3.4.2 The igniter 3.4.3 Design of the upper stage motor
4 Simulations 51 4.1 The simulation software 4.2 The motor performance prediction program 4.2.1 Klemmung calculation 4.2.2 Gas production and pressure calculations 4.2.3 Thrust calculation 4.2.4 Re-sampling 4.3 The flight simulation program 4.3.1 Assumptions of the simulation 4.3.2 Input data for the flight simulation program 4.3.3 The rocket geometrical parameters 4.3.4 Aerodynamic parameters. 4.3.5 Instantaneous mass of the model.
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.5 Moment of inertia model 4.3.6 The weather model 4.3.7 The reference frames 4.3.8 Forces on the rocket 4.3.9 Rotation 4.3.10 Acceleration, velocity and position viii 4.3.11 Simulation parameters
Table Contentsof 4.3.12 Flight simulation validation 4.3.13 Flight parameter optimization 4.3.14 Failure scenario simulation 4.3.15 Operational parameter simulation
5 Production 93 5.1 Production 5.2 Production planning
6 Flight and data analysis 99 6.1 The static tests of the rocket motors 6.1.1 The booster motors 6.1.1.1 Results of the booster motor tests 6.1.1.2 Comparison of the booster motor results with MPPT results 6.1.2 The second stage motor 6.1.2.1 Results of the second stage motor tests 6.1.2.2 Comparison of the second stage motor results with MPPT 6.2 Results of FTPS: the nominal flight trajectory 6.3 The launch 6.3.1 State changes 6.3.1.1 Conclusions from the state changes 6.3.2 ETAG 6.3.3 Doppler shift
7 Conclusions and recommendations 127 7.1 Conclusions 7.2 Recommendations
Bibliography 129
Mark Uitendaal B.Sc. M.Sc. Thesis
A The analytical results compared to the simulation 131 A.1 The analytical results compared to the simulation A.2 The booster burn-out velocity A.3 The velocity of second stage ignition A.4 The burnout velocity of the second stage
B The aerodynamic parameters 135 ix
B.1 The aerodynamic parameters as used in the simulations
C Performance plots of the nominal flight trajectory 139 C.1 Performance plots of the nominal flight trajectory
D The outline of the Stratos rocket 147
Table ofContents Table E The Epicote system 149
F ETAG data 153
. M.Sc. Thesis Mark Uitendaal B.Sc.
x Table Contentsof
Mark Uitendaal B.Sc. M.Sc. Thesis
Greek symbols xi
α Angle of attack [rad] γ Ratio between the specific heats [-] ζ Damping ratio [-] ζ Start-up variable [-] η Efficiency [-] Nomenclature θ Angle between inertial reference frame and body fixed reference frame [rad] λ Fixed geometrical ratio [-] ρ Density [kg/m 3] τ Vanderkerckhoven parameter [-] Ω Rotation rate [rad/s] Ω& Rotational acceleration [rad/s 2]
Latin symbols a Acceleration [m/s] A Area [m 2] a Burning rate [mm/s] 2 Aref Reference surface area of the rocket [m ] C* Characteristic exhaust velocity [m/s]
Caero Aerodynamic damping coefficient [-] Ccorrective Corrective moment coefficient [-] cd Drag coefficient [-] Cdamp Damping moment coefficient [-] Cjet Jet damping coefficient [-] cl Lift coefficient [-] Clα Lift slope coefficient [-] Cm Aerodynamic moment coefficient [-] Cnα Normal force slope coefficient [-] d Diameter [m] D Drag [N] F Force [N] G Geometrical ratio [-] g Gravitational acceleration [m/s 2] h Altitude [m] h Height [m] I Impulse [Ns] 4 Irocket Inertia of the rocket [m ] Isp Specific Impulse [s] 4 Ixx Inertia over x axis [m ] Kn Klemmung [-] l Length [m] M Mass [kg]
. M.Sc. Thesis Mark Uitendaal B.Sc.
M Mach number [-] m Mass of the grain [g] M Moment [Nm] m& Mass flow [Kg/s] n Pressure exponent [-] P Pressure [Pa] xii q Dynamic Pressure [Pa]
Nomenclature r Radius [mm] r Regression rate [mm/s] R Universal gas constant [-] s Surface area [m 2] s Distance [m] SM Static Margin [cal] T Temperature [K] t Thickness [mm] t Time [s] T Thrust [N] V Velocity [m/s] V Volume [m 3]
Vsound Speed of sound [m/s] W Weight [N] X Distance, position [mm] x Geometrical step [-] X X axis in reference frame [-] Y Y axis in reference frame [-] ∆t Time step [s]
Subscripts
0 Initial value e Effective e Empty 0 Sea level cp Centre of pressure cg Centre of gravity m Moment rail Launch rail ref Reference d Drag drogue Drogue parachute main Main parachute rp Reaction products c Chamber e Exit a Ambient a Aerodynamic b Body ab From aerodynamic to body bi From body to inertial i Inertial
Mark Uitendaal B.Sc. M.Sc. Thesis
Abbreviations
CANSAT CANister SATellite, a project of DARE CFRP Carbon Fibre Reinforced Plastic DARE Delft Aerospace Rocket Engineering xiii DARK Danish amateur rocketry group DMA Drogue Mortar Assembly DSA The glider society in Delft DSE Design Synthesis Exercise (Bachelor end-project) DUT Delft University of Technology EED Electro Explosive Device ETAG Esrange Throw Away GPS Nomenclature EWI Electrotechnical Engineering faculty at DUT FTPS Flight Trajectory Prediction Program GPS Global Positioning System I2C Inter-Integrated Circuit IMU Inertial Measurement Unit ISA International Standard Atmosphere MCU Master Control Unit MPPT Motor Perfromance Prediction Tool NAVRO Dutch Amateur Rocket Research Association PCB Printed Circuit Board PGA PyroGen Assembly PMB The metal workshop at the industrial Engineering facility SD Secure Digital SSA Stage Separation Assembly SVN Subversion software UART Universal Asynchrone Receiver/Transmitter
. M.Sc. Thesis Mark Uitendaal B.Sc.
1 At the 17th of March 2009, a rocket called Stratos was launched, by Delft Aerospace Rocket Engineering, or DARE for short. The purpose of this rocket was to break the European altitude record for amateur rockets which was at that time 10.7 km. The Stratos broke this record and soared to 12.551 km above its launch pad at Esrange Space Centre in Kiruna, Sweden.
The Stratos project was the biggest project attempted yet by DARE and the first time DARE Introduction had a successful sponsor-partnership with Dutch Space, a space company located in Leiden, the Netherlands. The Stratos rocket was the first non-professional rocket launched at Esrange, paving the way for DARE to launch bigger and more complex rockets at Esrange in the future.
Objective of the thesis
This master thesis is dedicated to the process of designing, simulating and production of the Stratos rocket. The report starts with a project objective, gives an overview of the design process and simulations and concludes with a comparison between the simulation and the results of the flight. The role of the author in the whole Stratos project was project initiator, project leader and responsible for rocket design, motor design and flight simulations. Since this is a thesis, only the work performed by the author is written down in the report.
The objective is to give a detailed insight in the design, the simulation tools, the production process and the results of the mission.
By far not all facets learned in this project can be captured in a technical report such as this thesis, but the technical details necessary for completing this project are included.
The Stratos project
The project was initiated in October 2007, initially with a team of over 20 persons. The project was originally intended to break the European Altitude record for amateur rockets, in a later stage of the project it became apparent that commercial payload needed to be implemented for financial reasons.
This payload was the IMU (Inertial Measurement Unit) designed by a group of students for the DSE (Design synthesis exercise) 2008. The IMU autonomously measures and stores acceleration and rotation data in order to reconstruct the trajectory of the vehicle.
The project switched to the production phase after October 2008, although the group slimmed down to 16 people. In total, 14 people traveled to the launch site in Sweden and successfully launched the Stratos rocket, reaching a new milestone for DARE and the Delft University of Technology (DUT).
. M.Sc. Thesis Mark Uitendaal B.Sc.
2 Introduction Introduction
Mark Uitendaal B.Sc. M.Sc. Thesis
In order to define a project, first a project objective needs to be set in order to be able to 3 determine the project requirements. The objectives and requirements for the Stratos project where determined and explored before the beginning of this graduation project.
The objective of the project can be split up into several parts:
objective ect • Break the European Altitude record for amateur rockets, which was 10.7 km at the proj
time –
• Expand the knowledge of DARE, and preserving this for future generation of students
1 Chapter • Increase the visibility of DARE within Delft University of Technology (DUT) and the space community.
• Launch at Esrange or Norange and explore the logistical steps necessary.
These objectives where set in the interest of DARE. The objectives are important for future work of DARE.
The European altitude record objective was chosen because of its high exposure. This would increase the chance of sponsorship contracts, important for DARE to continue such project of this magnitude.
The knowledge of DARE should be expanded in order to create bigger rockets and achieving higher altitudes. Project Stratos is a typical example of flight envelope expansion, being the first DARE rocket to go supersonic and higher than 1800 m, the previous altitude record of DARE.
The visibility of DARE within DUT could be increased, creating possibilities for a symbiosis between the university and the student society. In this way, the educative part of DARE can be incorporated within the curriculum, and students can have ”hands-on experience” with the theory learned at the university. The visibility of DARE within the space community can be helpful when searching for new sponsorship contracts.
With a launch at Esrange or Norange , DARE can explore the logistical hurdles to be taken when launching abroad. These rocket ranges, specially designed to accommodate professional sounding rockets, allow very high apogee altitudes. DARE strives to launch rocket to ever increasing altitudes, something which can only be done at these rocket ranges.
. M.Sc. Thesis Mark Uitendaal B.Sc.
4 Chapter 1 –Project objective
Mark Uitendaal B.Sc. M.Sc. Thesis
2.1 A brief introduction into rocket motion 5
A rocket stage burnout velocity in vacuum can be expressed by the rocket equation of
Konstantin Eduardovich Tsiolkovskii. A rocket vehicle is defined as a device that can apply design - acceleration to itself by expelling part of its mass with high speed in the opposite direction. This rocket equation is given in Equation 2.1.
M 2 Chapter 0 ∆Vburnout = Ve ln M e Equation 2.1
In which:
• Vburnout = burnout velocity [m/s] • M0 = initial mass [kg] • Me = burnout mass [kg] • Ve = effective exhaust velocity [m/s]
The effective exhaust velocity of a rocket can also be expressed as Equation 2.2.
V = I ⋅ g e sp 0 Equation 2.2
Where:
• Ve = effective exhaust velocity [m/s] • Isp = specific impulse [s] • 2 g0 = gravitational acceleration [m/s ]
In order to reach a high velocity, it can be seen that this can be reached by two strategies:
• Increase the effective exhaust velocity, which can be achieved by increasing the
specific impulse (I sp ) of the propulsion system
M • Increase the mass ratio 0 of the vehicle, which can be achieved by increasing the M e propellant mass fraction of the vehicle. In order to achieve this, the empty mass of the vehicle must be minimized and the propellant mass should be maximized.
With these formulas it can be calculated what the burnout velocity in vacuum without a gravitational field will be. However, sounding rockets fly through the earth’s atmosphere and in the gravitational field of the earth.
. M.Sc. Thesis Mark Uitendaal B.Sc.
The aerodynamics of the vehicle will determine the amount of energy bleed-off because of aerodynamic drag during the flight. During the flight the vehicle is decelerated by the gravitational acceleration.
For further increment of the burnout velocity another concept is explored: staging. A multistage rocket consists of two or more rocket stages, each with their own motor. When the 6 bottom propellant is spent, the rocket separates this part of the vehicle from the top stage.
Chapter- 2 design After separation, the propulsion system of the top stage is initiated. This is called tandem or serial staging. By jettisoning stages when they run out of propellant, the mass of the remaining rocket is decreased. This allows the thrust of the remaining stages to more easily accelerate the rocket to its burnout velocity and thus also gaining more altitude.
Mark Uitendaal B.Sc. M.Sc. Thesis
2.2 Motor burnout
After motor burnout the vehicle will no longer have thrust. Now the vehicle encounters only gravitational acceleration and aerodynamic drag. Under normal circumstances these vectors are not in the direction of the velocity vector and the vehicle is decelerated 7
The phases after motor burnout is called the coasting phase. In order to maximize the distance travelled during the coasting phase, the aerodynamic drag of the vehicle must be minimized. design -
During the coasting phase, only 3 forces apply on the rocket:
• Weight [N] 2 Chapter • Drag [N] • Lift [N]
Figure 2.1: the forces on the rocket during coasting
The weight of the vehicle, which is the mass of the vehicle multiplied by the gravitational acceleration.
The drag of the vehicle, which is the friction of the vehicle while travelling trough the atmosphere.
The lift of the vehicle is the side way forces if the rotational symmetric vehicle travels at an angle of attack through the atmosphere.
. M.Sc. Thesis Mark Uitendaal B.Sc.
2.3 Rocket stabilization and flight
The stabilization of all rockets made by DARE up to 2009 is passive. This means the rocket is aerodynamically stabilized. A statically stable vehicle is defined as [1] :
∆C 8 m < 0 ∆α Chapter- 2 design Equation 2.3
In which:
• ∆Cm = the differential of the aerodynamic moment • ∆α = the differential of the angle of attack
This can be achieved by positioning the centre of pressure behind the centre of gravity of the vehicle. Due to this fact, the rocket will automatically point its centreline into the local airflow direction.
Figure 2.2: the statical stability and the position of the centre of gravity and centre of pressure
Mark Uitendaal B.Sc. M.Sc. Thesis
The aerodynamics of the vehicle is determined by the surface which is exposed to the airflow or “the wetted surface”. The most important parameter in the aerodynamics of a rocket vehicle is known as the Static Margin [2]. The static margin of a rocket or missile is defined as:
X cp − X cg SM = d 9 Equation 2.4
Where:
design - • SM = static margin [calibres] • Xcp = the position of the centre of pressure from the tip of the nosecone [mm] • Xcg = the position of the centre of gravity from the tip of the nosecone [mm] • d = the diameter of the rocket [mm] 2 Chapter
The position of the centre of pressure of a vehicle is determined by three things:
• The aerodynamic shape of the vehicle. The combination of all the wetted surfaces of the vehicle will determine the position of the centre of pressure. If some wetted surface is de-attached from the vehicle, for instance a complete rocket stage, the position of the centre of pressure changes.
• The air speed of the vehicle. If the flow around the vehicle is incompressible, the position of the centre of pressure is fixed. At transonic and supersonic speeds the position of the centre of pressure can shift.
• The angle of attack of the vehicle. Depending on the fineness-ratio [3], at higher angles of attack, the position of the centre of pressure will shift backwards.
The position of the centre of gravity of the vehicle is determined by the distribution of mass throughout the vehicle. A rocket vehicle expels mass by definition, therefore most probably the position of the centre of gravity of the vehicle will alter during the operation of the propulsion system. During the coasting phase the position of gravity stays constant.
The fact that the vehicle is passively stabilized affects the design of the propulsion system. A high number of stages is not possible due to the possibility of arcing, because the rocket flight direction can not be corrected during flight. Another drawback of aerodynamic stabilization is the fact that the rocket needs to be stabilized in another way until the aerodynamic surfaces have effect. The aerodynamic surface needs some airflow in order to produce a corrective moment for course alterations. This initial stabilization is done via a launch rail. The length of the DARE launch rail is limited for practical reasons to 6 meters. This means the rocket needs to accelerate to a high velocity within these 6 meters, which poses a requirement on the initial acceleration of the rocket vehicle.
If the rocket leaves the tower in a condition with side wind, the statically stable rocket will rotate into the wind. This phenomenon is called weather cocking. The rocket will begin its flight trajectory with a little angle from vertical. This angle is called the kick angle. [4] For safety reasons the minimal tower exit velocity for any passively stabilized rocket must be 20 m/s [2].
. M.Sc. Thesis Mark Uitendaal B.Sc.
The initial minimum acceleration of the vehicle can be expressed as:
Vexit srail ∫V ⋅ dV = ∫ a ⋅ ds 0 0 Equation 2.5 10
Chapter- 2 design Where:
• V = velocity of the vehicle [m/s] • a = acceleration of the vehicle [m/s 2] • s = total length of the launch rail [m]
This results in a minimum acceleration of 33 m/s 2 in order to satisfy the safety requirement. However, in order to reduce the kick angle due to weather cocking against the wind, the tower exit velocity needs to be high.
For the Stratos rocket, which purpose it is to reach the highest altitude possible, the kick angle of the vehicle must be kept to a minimum. Therefore it is chosen in the design to have a very high initial acceleration. The tower exit velocity of the final rocket design is more than 35 m/s .
Mark Uitendaal B.Sc. M.Sc. Thesis
2.4 The rocket design
In order to minimize the risk of arcing during flight, for the Stratos vehicle it was chosen to have only two stages: 11 • The booster stage should initiate a high acceleration in order leave the launch rail at
high velocity. In order to do this it needs to develop huge amount of thrust in a very short burn time design
-
• The main stage needs to develop a high burnout velocity at a high altitude.
Chapter 2 Chapter
Figure 2.3: the Stratos vehicle split up into two stages.
The two stages enable a simple break up of the booster – sustainer [5] principle of a solid rocket motor, optimizing motor design. The staging enables a higher burnout velocity of the second stage, which enables longer coasting distance.
. M.Sc. Thesis Mark Uitendaal B.Sc.
In order to provide insight in the design, the Stratos vehicle is split up further into three parts as can be seen in Figure 2.4:
12 Chapter- 2 design
Figure 2.4: a component breakdown of the Stratos vehicle.
• The main purpose of the booster stage is the initial acceleration to a high tower exit velocity. After the usage of this stage, it is jettisoned. The booster stage is not equipped with a parachute recovery and is destroyed upon impact. A detailed overview of the booster section can be found in Figure 2.5.
• The main stage: this stage works after the booster stage is jettisoned and consist of two sections: the sustainer section and the capsule section:
1. The sustainer section is the solid rocket motor of the main stage. It provides thrust and stability during the second stage burn phase of the flight, thrusting the vehicle up to its final burnout velocity. In the coasting phase it provides aerodynamic stability for the main stage of the vehicle. The sustainer section is discarded after drogue parachute deployment. The sustainer section is destroyed upon impact. A detailed overview of the sustainer section can be found in Figure 2.6.
2. The capsule section: this section controls the whole vehicle, covers the payload and is recovered by parachute in order to be retrieved. A detailed overview of the capsule section can be found in 2.4.3 – The capsule section.
Mark Uitendaal B.Sc. M.Sc. Thesis
2.4.1 The booster stage:
The booster stage of the Stratos vehicle is specifically designed to produce a high amount of thrust, in a short time. The structural mass of this part of the vehicle is kept to a minimum. This part of the vehicle is deliberately not equipped with a parachute system, in order to save mass. 13
The booster stage is built up out of a cluster of four motors. This amount is chosen for
geometrical reasons, in order to have the lowest frontal area in combination with the four fins. design -
The clustered motor configuration has several advantages over a single motor:
•
High thrust 2 Chapter • Short thrust duration • Small stage length • Manufacturing advantages
High thrust . Because the now four grains cores instead of one, the burning area in the motor can be high in combination with Bates grain configuration. This Bates configuration was selected for manufacturing reasons. This enables high mass-flow in combination with a short stage length.
Short thrust duration . Because the smaller web thickness 1, a motor with a Bates configuration and a small diameter can burn shorter then one of a bigger diameter. This enables to design a stage with shorter burn time and high thrust.
Small stage length . In order to reduce the possibility of aeroelastic behaviour in flight, the specific stiffness of the rocket should be as high as possible. In order to accomplish this is the total length of the rocket should be small
Manufacturing advantages . The propellant can be cast in smaller batches. Casting smaller grains has some manufacturing advantages with respect to grain shrinkage, over bigger grains.
The clustered motor option also has some disadvantages:
• Possibilty of a misfire of one of the motors • Same thrustlevels requirements • Specific stiffness
The possibility of a misfire . The reliability of motor ignition should be very high in order to ensure full ignition on all the four motors.
The thrust levels in all four motors should not differ much. This is because four motors should cooperate simultaneously, ensuring no deviations in the trajectory of the rocket.
The specific stiffness of the vehicle is reduced, because the second moment of inertia per mass unit is lower in the clustered variant than the circular variant.
1 See chapter 4 - Simulations
. M.Sc. Thesis Mark Uitendaal B.Sc.
The booster stage is designed to work for only 3.5 sec and to accelerate the vehicle to almost Mach 1. Since the booster stage is destroyed on impact, the production cost of this stage will have to be as low as possible. Because of this requirement, together with the minimum mass requirement, the amount of components is reduced to a minimum. This results in a lower production costs and structural mass. The downside of this approach is the absence of an 14 aerodynamic fairing, creating a less efficient aerodynamic shape and thus a higher aerodynamic
Chapter- 2 design drag coefficient.
The booster stage can be split up into several parts, as can be seen in Figure 2.5.
Figure 2.5: a component breakdown of the Stratos booster stage:
The launch lugs is the mechanical interface with the launch tower. The Stratos rocket is aerodynamically stabilized; therefore the vehicle will only perform stable flight when air is flowing around its aerodynamic surfaces. The launch lugs of the vehicle will guide the rocket in the rail up to a velocity of around 36 m/s.
The booster motor is the actual part that provides the thrust. Four motors are used in the booster stage in order to provide use amounts of thrust in a short time, within a small length.
The fin section provides the stability of the vehicle in two stage configuration.
The clamp band : is added in order to provide structural support for the booster motors. The motors are clamped sideways by this clamp band by the band and a strong epoxy adhesive.
The interstage coupler is for the connection between the booster stage and the main stage of the vehicle. The interstage coupler itself consists of two parts: the structure itself and the aerodynamic fairing.
The structure is made entirely out of aluminium. The design of the interstage structure is focused on the manufacturing of the part, so the whole load carrying structure is made out of several rotational symmetric parts which can be produced with a lathe. The disadvantage of such design is that it is
The aerodynamic fairing is made out of foam and glass fibre composite and is for aerodynamic purposes only.
Mark Uitendaal B.Sc. M.Sc. Thesis
2.4.2 The main stage:
This stage is the second stage of the entire vehicle. This stage needs to have a high specific impulse and a high propellant mass fraction to maximize the burnout velocity of the vehicle. The aerodynamics of this vehicle are also very important this is the main driver in the design because of the very high speeds involved in this stage. 15
In order to reduce the aerodynamic drag of the vehicle, the drag coefficient and the cross- sectional area must be minimized. This can be done by selecting the most optimal
aerodynamic shape of the vehicle. design -
The main stage consists of two parts:
• Sustainer section 2 Chapter • Capsule section
In order to increase the mass ratio of the vehicle, only the most essential parts of the vehicle should be recovered. The less mass that is needed to be recovered, the lower mass is needed for the recovery system. This lowers the overall structural-mass by minimizing the mass associated with the recovery system.
After motor burnout, the rocket is decelerated by two factors:
• Gravitational acceleration: the gravitational pull of the earth is decelerating the vehicle. The local gravitational acceleration with respect to the valid flight envelope is approximately 9.81 m/s 2
• Aerodynamic drag: the aerodynamic forces on the rocket are decelerating the vehicle.
The aerodynamic drag of the vehicle can be expressed in:
D = cd ⋅ Aref ⋅ q Equation 2.6
In which
• D = aerodynamic drag force [N] • cd = the drag coefficient [-] 2 • Aref = the reference area of the vehicle, which is the frontal area in rocketry [m ] • q = dynamic pressure [Pa] Equation 2.7
. M.Sc. Thesis Mark Uitendaal B.Sc.
The c d of the vehicle incorporates all sorts of airflow vehicle interactions where the most common are:
• Friction drag • Pressure drag • 16 Wave drag • Induced drag Chapter- 2 design
Friction drag : the drag caused by the shear forces between the skin and air-particles flowing over the wetted area of the vehicle.
Pressure drag : caused by the geometric shape of the vehicle travelling trough the air particles.
Wave drag : the drag caused by the vehicle travelling at supersonic speeds. The energy which is radiated away from the vehicle in the form of shockwaves is experienced as drag.
Induced drag : caused by the fact that the aerodynamic surfaces of the vehicle generate lift when inclined at an angle of attack. This lift comes with the associated induced drag. If the angle of attack is zero, such which is the case in stabile flight, the lift and thus the induced drag will be zero.
The dynamic pressure is defined as the dynamic pressure:
q = 1 ⋅ ρ ⋅V 2 2 Equation 2.7
In which:
• q = dynamic pressure [Pa] • ρ = density of the medium, in this case air [kg/m 3] • V = velocity of the vehicle [m/s]
Mark Uitendaal B.Sc. M.Sc. Thesis
2.4.2.1 The sustainer section
The sustainer section can be split up into several parts, as can be seen in Figure 2.6.
17
design -
Chapter 2 Chapter
Figure 2.6: a component breakdown of the sustainer section of the second stage of the Stratos
The fin section is manufactured out of 6 mm carbon fibre sheet. The aerodynamic shape is designed for flutter resistance. The leading and trailing edges of the fins are canted with a 10° edge, which is as a standard supersonic profile [3] .
The sustainer motor , or second stage motor is the propulsion system of the second stage. This motor is described in detail in section 3.4 -The upper stage motor design.
The pyrogen is the igniter of the sustainer motor. This igniter is described in detail in section 3.4.2 - The igniter.
The Stage Separation Assembly or SSA is the device responsible for the separation of the booster stage and the main stage. The booster stage has a larger frontal surface area, therefore this stage has more aerodynamic drag than the main stage. The stages will separate due to drag separation [2]
The capsule section with all the flight computers and recovery devices is the nosecone of the vehicle.
. M.Sc. Thesis Mark Uitendaal B.Sc.
2.4.2.2 The capsule section
The capsule section can be split up into several parts, such as can be seen in Figure 2.7.
18 Chapter- 2 design
Figure 2.7: a component breakdown of the capsule section
The parachute section is the whole assembly responsible for the recovery of the capsule section. This section consists of the drogue mortar and a parachute activation deck. The drogue mortar, which is essentially also the coupler between the capsule section and the sustainer section, also holds the parachute. The parachute system design is further elaborated in section 2.5 - Recovery.
The fairing is the aerodynamic shell of the capsule section. The aerodynamic shape of the fairing is a Sears-Haack body, a shape optimized for the transonic speed regime in which it needs to operate [3]. This aerodynamic shape is also chosen because of manufacturing considerations. A thin-walled glass-fibre fairing in this shape was bought and reinforced.
The fairing has a number of interfaces with the environment. The vehicle needs connectors for external power and data transfer and safe/arm plugs. Another important interface with its environment is the static ports. These ports equalise the inside pressure with the ambient pressure. In the fairing there are three ports under 120 ° rotation with a diameter of 2 mm.
To set a requirement for bleeding air out of the volume, it is chosen to satisfy at least the ESA Envisat requirement [6].
A − ≥ 20 ⋅10 4 1 V m Equation 2.8
Mark Uitendaal B.Sc. M.Sc. Thesis
Where:
• A = the surface area of the static ports [m 2] • V = the volume which needs to be drained [m 3]
The three ports of 2 mm diameter satisfy this requirement by a factor of 2. 19 The flight computers and payload section are the controllers of the vehicle. The actuation of several important devices, such as the second stage separation, second stage motor ignition
and parachute ejection. This part was produced as a stand alone part, in order to design - accommodate tinkering with the electronics and to be able to work in different workshops with stand alone parts. The flight computers and payload of the capsule section can be split up into 4 parts as can be seen in Figure 2.8. Chapter 2 Chapter
Figure 2.8: a component break down of the complete electronics suite of the Stratos vehicle
The DARE flight computers are controlling the vehicle. The separate boards are connected via I2C and/or UART connection. The flight computer consists of several parts:
• MCU board • Measurements board • Data storage board • Pyro-board • Servo actuation board • Telemetry board • Power board
The MCU or Master Control Unit controls the separate boards. The flight sequence of the MCU is composed out of several states as can be seen in Figure 2.9.
. M.Sc. Thesis Mark Uitendaal B.Sc.
Figure 2.9: the flight sequence of the Stratos flight computer.
20 The MCU can only switch states via two constrains: the measurement board flags the MCU,
Chapter- 2 design or the internal timing mask of the MCU switches the state. This timing mask approach was chosen in order have a so called “nominal flight program”. If the sensor data from one of the two measurement boards deviates from this nominal program, the sensor reading is classified as false. If both measurement boards produce sensor-data which doesn’t match the timing mask, the flight is aborted.
The Measurement board is a fully redundant sensor package of 2 air pressure sensors and a three- axis acceleration sensor.
The data storage board stores all measurements in a mini SD-card of 2 Gb. The board is connected directly to the measurement boards via a UART data connection.
The pyro board actuates all the pyrotechnical components. This board is fully redundant and has a separate power source for each pyro board. The whole pyrotechnic chain of the vehicle is further elaborated in section 2.6 - Pyrotechnics of the vehicle.
The servo actuation board is responsible for actuating the servo of the pin puller system.
The telemetry board is for transmitting valuable data to the ground via radio. This was done by transmitting basic housekeeping data by a standardized beeping code. The operating frequency of the radio was 433.92 MHz.
The power board is responsible for transferring power from the batteries to the different boards. This board also does the switching between internal and external power.
The DSE payload is a payload from the TU Delft. This payload was the result of the DSE exercise 2008 group 18. The payload is a complete stand alone unit with an Inertial Measurement Unit (IMU) and data recorder. The IMU can measure accelerations and rotations in 3 axes.
The ETAG module is a stand alone beacon working with the Global Positioning System (GPS) the GPS is a satellite based positioning system, which can be accurate within meters. The ETAG module also broadcasts the GPS position on via radio on the 173.225 MHz frequency. This frequency, also known as the E-link system, can be received by Esrange and the GPS position is stored for rocket recovery purposes.
The structure of the electronics module provides support of the electronics. The loads that the electronics can encounter are handling loads, launch loads, recovery loads and impact loads. The electronics are attached to the structure by a glass fibre base-plate. The material of the base-plate was selected as glass fibre because of radio transparency and structural stiffness.
Mark Uitendaal B.Sc. M.Sc. Thesis
2.5 Recovery
Some parts of the vehicle contain valuable data or expensive equipment. These parts need to be recovered. The recovery system of rocket parts of a small sounding rocket should decelerate the part to a suitable impact velocity, or otherwise ensure that the acceleration of 21 the part during impact is not such that the important equipment of the vehicle is damaged.
For the Stratos rocket several recovery design options were considered:
design - • Single stage parachute recovery; this option is the most common and also frequently used by DARE. A parachute will provide more drag, which will decelerate the recovered part to a slower speed. This has as an advantage that it is a very simple and
low mass and low volume. However, since such a system depends on dynamic 2 Chapter pressure, the deployment accelerations and envelope are variable.
• Dual stage parachute recovery; has the same advantages as above. The system deploys a very small parachute to decelerate the part to a lower airspeed. At another specified moment in time a bigger parachute will take over. The volume and mass of such a system are slightly higher, but the deployment accelerations are lower are and usage envelope is higher. The usage envelope is specified as the circumstances on which the system can operate.
• Parachute recovery with airbag; this option is a variant of the previous option. However, it is possible to lower the impact accelerations by using some sort of inflatable cushioning device. The parachute canopy can thus be smaller, reducing the deployment loads. On the downside, mass and volume are higher, and it also requires the presence of a pressurized system or other type of gas generator, scoring lower on safety.
• Parachute recovery with retro rocket motors. This is basically a variant on the airbag type, only several meters above ground the rocket part is decelerated further by one or several rocket motors in order to reduce the impact loads on the part. Downside of this design is the addition of another pyrotechnical system in the rocket, with associated mass, volume, complexity and safety considerations.
Exotic recovery options such as tumble recovery with airbag, gyro-recovery or impact poles are not considered because a very low technology readiness level, or overall lack of feasibility within the timeframe of the project.
Table 2.1: the selected recovery options in a trade off table Option\Criteria Safety Mass Volume Deployment loads Usage envelope Weight 2 1 0.5 1 0.5 Single stage parachute High Low Low High Low Dual parachute High Medium Medium Low High Parachute with airbag Medium High Medium Low High parachute with retro-motors Medium High High Low High
. M.Sc. Thesis Mark Uitendaal B.Sc.
It can be seen from Table 2.1 that the safety aspect of the system is always of great importance to the operators of the vehicle. It is preferred to use as little pyrotechnical systems as possible. The parachutes of Stratos can be actuated by an electromechanical system, or by a pyrotechnical system. Thereby initially this system receives a high safety grade. The airbag system definitely needs some sort of gas-production for inflation. This can be done electromechanical with a pressure vessel or pyrotechnically, thereby receiving a medium grade 22 for safety
Chapter- 2 design The single stage parachute can’t operate at high dynamic pressures and high wind velocities (because of drifting with the wind, due to the long parachute hang time)
From Table 2.1, it can be concluded that a dual stage parachute system is the preferred option, due to higher safety, medium mass and volume and good deployment loads and usage envelope.
Mark Uitendaal B.Sc. M.Sc. Thesis
2.5.1 Capsule separation and recovery
Because of mass constraints the capsule section is the only part of the Stratos rocket which is equipped with a recovery device. For that reason, the capsule section is separated from the rest of the main stage fuselage. In order to do this, a capsule separation system needs to be designed. This system needs to be safe, have a low mass and volume and have a high usage 23 envelope. design -
Chapter 2 Chapter
Figure 2.10: capsule separation of the Stratos.
Several methods of separation were identified:
• Pyrotechnical system; a system which produces gas with a pyrotechnical gas generator in order to separate the two parts.
• A pressurized system; this is the same kind of system as described above, but it is operated via a pressure vessel and a electromechanically operated valve.
• A purely electromechanical system; for example some sort of spring loaded system which is de-blocked electromechanically.
The three options are evaluated in a trade off process, which can be seen in Table 2.2.
Table 2.2: The selected seperation options in a trade off table Option\Criteria Safety Mass Volume Usage envelope Complexity Certification Weight 2 1 0.5 1 0.5 1 Pyrotechnical seperation Medium Low Low Low Low Low Pressure system seperation High Medium Medium High Medium High Electromechanical seperation High High Medium High High Low
The use of high explosives, such as RDX, HMX or PETN is restricted by law. Due to this restriction, DARE only uses blackpowder for its pyrotechnics.
Blackpowder has a very high pressure exponent (n), which means the regression rate of the charge reduces dramatically in lower ambient pressures. This means that at higher altitudes the probability of successful separation is diminished. The usage envelope of such a pyrotechnical
. M.Sc. Thesis Mark Uitendaal B.Sc.
system for the Stratos project is lower. Due to the lower static pressure, the chances of a successful separation are diminishing at an altitude higher than 4000 meter.
The complexity of a separation and recovery system is twofold; the system is hard to produce, but also the system is more prone to failure, due to vibrations or accelerations.
24 The certification of the pressure system is more difficult because the pressure vessel needs to
Chapter- 2 design be certified in order to be launched at Esrange. The pressure vessel itself can be bought from a supplier, but this is not a guarantee for correct certification.
Since safety is one of the driving requirements of the design process of the Stratos rocket, the pressure system was chosen as the most appropriate for the capsule separation. As time progressed in the design process, the certification and the human recourses in the team were not available. This was the reason why the first option: the pyrotechnical separation system was chosen in the end. This had a large effect on the maximum separation altitude of the system which was now set on approximately 4000 meters.
The point are drawn into a nominal flight trajectory, as can be seen in Figure 2.11, Point I representing the altitude possible with a pressure system, point II the separation altitude possible with a pyrotechnical system.
Figure 2.11: recovery points for the Stratos capsule, with various systems
Mark Uitendaal B.Sc. M.Sc. Thesis
When the separation has taken place, the capsule needs to deploy its recovery system.
The maximum force that a parachute can encounter is defined as:
F = c ⋅ q ⋅ s max d 25 Equation 2.9
In which:
design - • cd = the drag coefficient of the parachute. For cross shaped parachutes this is defined as 0.8 [2], calculated over the frontal area of the parachute [-] • s = the frontal area of the parachute [m 2]
• q = dynamic pressure [Pa] 2 Chapter
Where q is defined as the dynamic pressure:
q = 1 ⋅ ρ ⋅V 2 2 Equation 2.10
Where:
• q = dynamic pressure [Pa] • ρ = density of the medium, in this case air [kg/m 3] • V = velocity of the vehicle [m/s]
The surface area s is the area of the parachute. This area can be defined as the projected area of the parachute when in operation, or the flat area of the parachute on the ground, depending how the c d of the parachute is defined.
The dynamic pressure q increases dramatically during the post apogee stage, because the vehicle picks up velocity after apogee. This poses large stresses on the parachute recovery system.
The main parachute is activated when the vehicle is completely decelerated to the proper main parachute deployment velocity by the drogue parachute. It is now possible to calculate the maximum deployment force on the shock cord of the main parachute by rewriting Equation 2.9 by filling in the dynamic pressure when the drogue parachute has gone its steady state descent velocity.
c ⋅ s d drogue drogue F = ⋅ cd main ⋅ smain max m ⋅ g capsule 0 Equation 2.11
. M.Sc. Thesis Mark Uitendaal B.Sc.
In which:
• cd drogue = the drag coefficient of the drogue parachute (0.8) [-] • 2 sdrogue = the frontal surface area of the drogue parachute [m ] • 26 mcapsule = the mass of the capsule [kg] • cd main = the drag coefficient of the main parachute (0.8) [-] Chapter- 2 design • 2 smain = the frontal surface area of the main parachute [m ]
By setting the m capsule to constant, it can be seen that the design of the drogue and main parachute are connected. A bigger surface area on the drogue will lower the deployment load on the main parachute. However, the deployment load on a big drogue parachute is be huge when deployed on lower altitude.
The deployment load of the drogue parachute of the vehicle is set to a maximum of about 1500 N, which does not imply special material requirements or constructions.
The drogue parachute should be able to fit between the second stage motor endcap and the coupler of the nosecone, a cylindrical shaped volume of only 95 mm diameter and 30 mm height
The surface area of the parachute of Stratos is set to 0.05 m2, which corresponds to a cross- shaped [2] parachute with sides of 100 mm. This design has a very low packing volume, satisfying the packing requirements within the rocket. For the Stratos rocket the parachute ejection point vs. recovery forces can be seen in Figure 2.12.
Figure 2.12: the maximum shock cord tension during deployment vs the deployment altitude in a nominal simulated flight of Stratos.
It can clearly be seen from Figure 2.12 that from apogee to about 4500 meters the deployment loads are progressing. From an altitude of approximately 4500 meters the dynamic pressure is approximately constant.
Mark Uitendaal B.Sc. M.Sc. Thesis
This implies that the drogue parachute is always at deployed at the maximum dynamic pressure and maximum load.
The drogue parachute and recovered load is now completely defined as:
• Surface area, s: 0.05 m 2 27
• Drag coefficient, C d = 0.8 (cross shape parachute [2])
design - • Mass of the recovered item, m capsule = 3.8 kg
The maximum impact velocity of the main parachute has been set to 13 m/s, which the
assumption is made that the glass fibre fairing of the nosecone section will absorb the impact 2 Chapter shock and the flight computer of the vehicle will survive the impact.
The surface area of the main parachute can now be calculated via:
mcapsule ⋅ g s = 0 = 0.45 m 2 1 ⋅ ρ ⋅V 2 ⋅ c 2 d
Equation 2.12
In which:
• s = the surface area of the main parachute [m 2] • mcapsule = mass of the capsule [kg] • 2 g0 = gravitational acceleration [m/s ] • ρ = density of the medium, in this case air [kg/m 3] • V = velocity of the vehicle [m/s] • cd = drag coefficient of the parachute [-]
For the given values the surface area corresponds to a cross shaped drogue parachute with the side length of 300 mm.
Figure 2.13: the main parachute deployment sequence of the Stratos capsule
. M.Sc. Thesis Mark Uitendaal B.Sc.
2.5.2 Parachute activation
In order to keep the modularity in the design the activation of the parachute of Stratos is designed as a separate deck, the “parachute activation deck”. The parachute activation deck is designed with several aspects in mind: 28
Chapter- 2 design • Safety when operating with the vehicle • Cope with parachute deployment stresses • Mass and volume • Ease of use in preparation operation
Safety is the driving requirement in the whole project. The parachute activation deck contains some pyrotechnics which are safety hazards. The parachute activation deck is designed in such way that the human contact with the pyrotechnics is kept to a minimum.
The parachute activation deck should be able to cope with stresses associated with ejection and drogue and main parachute deployment. As can be seen from Figure 2.12, the forces of the drogue parachute that can be expected are high. The parachute activation deck must be able handle these forces and distribute those forces to the rest of the structure.
The parachute activation deck should be of low mass and low volume of the part . The mass of the part should be kept to the minimum, overall optimizing the mass-ratio of the vehicle. An overall bigger of the parachute activation system volume will take up mass, because the skin of the vehicle will take up mass.
Ease of use in preparation operation can be increased by keeping modularity. Since multiple teams will handle different parts of the capsule section, it is very wise to be able to split up the capsule section into segments. The individual segments can be handled by each team, enabling multiple manufacturing areas. The final assembly can be done when each team has completed its individual component.
Mark Uitendaal B.Sc. M.Sc. Thesis
The parachute activation deck of Stratos consists of a pinpuller assembly which can release the drogue parachute and a redundant set of pyrotechnical gas generators, otherwise known as pyro charges. This drogue parachute will pull out the deployment bag of the main parachute.
29
design -
Chapter 2 Chapter
Figure 2.14: the structural breakdown of the parachute activation deck
The deployment bag is made out NOMEX 2™, which shields the parachute from the heat and reactive residual components of the blackpowder separation charge. The NOMEX deployment bag is dimensioned such that it contains the shock cord, shroud lines and canopy of the main parachute.
2 NOMEX is a registered trademark by Dupont.
. M.Sc. Thesis Mark Uitendaal B.Sc.
30 Chapter- 2 design
Figure 2.15: the parachute activation deck with the positioning of its components
The drogue parachute is shielded by a small patch of NOMEX against the thermal loads associated with activation of the pyrotechnical gas generators [2].
Mark Uitendaal B.Sc. M.Sc. Thesis
2.6 The Pyrotechnics of the vehicle.
Pyrotechnics is the science of materials capable of undergoing self-contained and self-sustained exothermic chemical reactions for the production of heat or gas. 31 The pyrotechnics in the vehicle consist of two parts:
• The rocket propellant. The rocket motors are filled with rocket propellant which is in design
essence an explosive, however it cannot be detonated. -
• The Electro Explosive Devices, or EEDs. This device initiates a pyrotechnical chain, which causes some sort of action such as motor ignition or separation.
2 Chapter All EEDs within the vehicle can be divided into two types:
• External EEDs, which are EEDs not controlled by the vehicle. The only external EEDs in the Stratos rocket are the igniters of the booster, which are controlled by the central firing line of Esrange
• Internal EEDs, which are controlled by the vehicle’s flight computers. These are used for the separation of the stages, the nosecone separation and the ignition of the second stage.
A schematic of the all the EEDs in the Stratos vehicle can be found in Figure 2.16
Figure 2.16: all EED components in the Stratos vehicle
. M.Sc. Thesis Mark Uitendaal B.Sc.
The internal EEDs in the Stratos vehicle can be divided into two types:
The gas generators:
• Stage Separation Assembly or SSA: a redundant pair of squib in a charge of blackpowder. 32
Chapter- 2 design • The Drogue Mortar Assembly or DMA: a redundant pyrocharge of blackpowder in the pyro activation deck
The motor igniter:
• The pyrogen of the second stage motor (PGA).
In order to give an example of an EED, the Pyrogen igniter of the second stage motor design is explained.
Figure 2.17: the pyrogen in the second stage motor.
The pyrogen of the second stage motor is designed to contain 5 grams of blackpowder. This amount is empirically determined on:
• The inside initial free volume of the motor • The exposed surface area of the grains • The inhibited surface of the smoke grain • The lower static pressure conditions when the second stage is ignited
During testing of this motor at sea level conditions the amount of blackpowder proved to be sufficient, igniting the motor in such way that the thrust-up of the motor would be in 2 seconds as can be seen in the motor results in chapter 6.
Mark Uitendaal B.Sc. M.Sc. Thesis
The EEDs can be characterised by the presence of a squib. This component is the link between the electrical subsystem and the pyrotechnical subsystem. The squibs for every EED used by DARE for the Stratos vehicle is the Davey Bickford 1080 A00 igniter.
The characteristics of the Davey Bickford 1080 A00 igniter are listed in Table 3. 33
Table 2.3: the characteristics of the Davy Bickford 1080 A 00 igniter Quantity Value Unit
Resistance 0.18 ± 0.03 Ω design - No-fire current (10 s) 1.25 A All-fire current (3 ms) 4.60 A Maximum no-fire energy 50 mJ Minimum fire energy 85 mJ 2 Chapter Recommended fire current (40 ms) > 3.50 A Test current 10 mA
This type of squib was selected because of two reasons:
• To satisfy the Esrange requirement to have a minimal “no-fire current” of 1.0 Amp.
• To fit the same geometrical shape as the cheaper Davey Bickford 1042 A00 igniter, which was used during static testing during the begin of the project.
The total firing sequence of the EEDs within the Stratos vehicle can be seen in Figure 2.18, which gives the example of the firing sequence of the second stage motor.
Figure 2.18: the firing sequence of the second stage motor throughout the different subsystems.
The MCU, or Master Control Unit is the central brain of the vehicle. This unit is bases its decision on the measurement boards and its internal timing mask. The MCU commands the pyro-board, a dedicated unit to fire the squibs. The squibs where fired with a redundant pair of three-cell LiPo batteries of 1100 mAh. A full scale breakdown structure can be seen in Figure 2.20.
In order to control the voltage on the pyro board there is a arming plug between the pyro board and its power source, the pyro battery. Also between the squibs of the pyrogen and the pyro board is a take-off shunt. This take-off shunt is a break wire which prevents accidental ignition due to sway currents or false triggering on the platform while people are in close contact with the vehicle. A picture of the take-off shunt on the actual Stratos rocket can be seen in Figure 2.19.
. M.Sc. Thesis Mark Uitendaal B.Sc.
34 Chapter- 2 design
Figure 2.19: the take-off shunt, which prevents accidental ignition of the PGA on the platform in close contact with people (Picture Olga Motsyk, DARE)
Mark Uitendaal B.Sc. M.Sc. Thesis
35
design -
Chapter 2 Chapter
Figure 2.20: the hierarchy of the pyro system in the Stratos.
. M.Sc. Thesis Mark Uitendaal B.Sc.
36 Chapter- 2 design
Mark Uitendaal B.Sc. M.Sc. Thesis
3.1 Propulsion 37
Propulsion is associated with changing linear momentum of a body via a force acting on this body (action =
reaction). Derived from Latin: ‘pro’ means forwards and ‘pellere’ means to drive. A propulsion system produces design thrust to push an object forward [7]. 3.2 Propulsion options and requirements Propulsion
- In order to propel a vehicle some sort of propulsion system is needed in order to provide thrust and accelerate the vehicle, ultimately resulting in breaking the amateur altitude record. The most obvious choice would be to use an air breathing stage, since the vehicle will fly through dense, oxygen-rich atmosphere. However, the ultimate goal of DARE is to propel Chapter3 vehicles to higher altitudes, where such benefits do not exist.
Therefore, the air breathing stage is not an option for the Stratos rocket. However, the booster section of the Stratos could be an air breathing stage, because of its lower operation altitude. Due to its lower technology readiness level, an air breathing booster stage was not considered.
Figure 3.1: the propulsion options for Stratos
The real difference between air breathing propulsion and rocket propulsion is the fact that rockets carry there own oxidizing agent with them. The rocket propulsion options are summarized as follows:
• Liquid propellant • Hybrid propellant • Solid Propellant
. M.Sc. Thesis Mark Uitendaal B.Sc.
Liquid propellant is especially suitable for high impulse missions since the specific impulse (Isp) of liquid propellants are in general very high, in the range of 400 sec [5]. Practical use of liquid propellant in amateur rockets is very sporadic due to the extremely high complexity of the system and other practical problems such as manufacturability and material cost.
Hybrid propellants are somewhat more used into amateur rocketry, mainly because of there legal 38 advantage. Since a propellant is rated as an explosive by law only when the oxidiser is mixed 1 Chapter 3 –Propulsion design with the fuel, the hybrid motor is only “hazardous ” when in operation. Most of the time, hybrid propellants are relatively good performing propellants with respect to solid propellants, and can deliver an Isp of up to 400 sec [5], although most amateur system seen today are rating an Isp of 200 sec.
The solid propellant is the most common option used in amateur rocketry. The propellant is storable and easy to manufacture. Another advantage is relative high degree of “stand alone”. A solid rocket motor needs the least amount of ground support equipment. This type of propellant has to be handled with care because the oxidiser and fuel are already mixed, therefore increasing the risk. The fact that solid propellant is an explosive according to law is downside on the transportability.
The three options were assessed with a trade off process, which can be seen in Table 3.1.
Table 3.1: a trade off table of the rocket propulsion options for the Stratos rocket Option\Criteria Safety Mass ratio Isp Transportability Complexity Cost TRL Weight 2 0.75 1.25 1 1 1 2 Liquid Medium Low High High High High Low Hybrid Medium Medium Medium High High Medium Low Solid Medium Low Low Low Low Low High
In amateur rocketry, the availability of materials, the facilities and processes by which rocket propellants and motors may be produced, as well as available financing, is of big variety. As such, a clear distinction must be made between the needs of a professional rocket motor manufacturer and that of an amateur, with regard to requirements defining an ideal rocket propellant type. The Technology Readiness Level is an important factor for short term projects such as Stratos.
The solid propulsion option is best option to satisfy the requirements of Stratos mainly because the Technology Readiness Level is high. Consequently, the transportation to the launch site will be difficult; therefore this was identified as a focal point throughout the project.
The solid propellant used in the booster motors and the second stage motor of the Stratos rocket is the Potassium nitrate/Sorbitol propellant [2].
1 According to the law. In fact, the pressurised feed system could pose a danger to surroundings any time.
Mark Uitendaal B.Sc. M.Sc. Thesis
3.3 Booster motor design
The booster motor is specially designed to provide a large amount of impulse in a short time, thereby giving high levels of thrust. The motor is designed with the following requirements:
39 • Safety, the safety of a motor is defined as safety for people during manufacturing and operation of the rocket motor. Because of the high tower exit velocity, the high initial thrust is also a safety requirement, since it decreases the dispersion area.
design • Reliability, the performance of the motors should be reliable. The clustered motor configuration in the booster section requires similarity in thrust levels, impulse and burn time. Propulsion
-
M full • Performance, the motors should have a very high propellant mass-ratio and M empty
a high specific impulse (I sp ). Chapter3
• Cost, the cost per motor should be kept to a minimum, enabling to do more static tests within in the project-budget.
The mass ratio of a motor can also be written as:
M full M propellant + M ca g = sin M M empty ca sin g Equation 3.1
It can be seen from Equation 3.1 that in order to maximize the mass ratio, the mass of the casing should be minimized and the mass of the propellant should be maximized.
In order to stay within the certifications of the propellant the sorbitol propellant [2] is used in the booster motor.
. M.Sc. Thesis Mark Uitendaal B.Sc.
For solid propulsion the desired thrust profile for the motor is the driving requirement for dimensioning the grain. The grain shape for the sorbitol propellant is limited by the fact that complex core-shapes are almost impossible to produce with the current technology. The preferred option is just to use a circular core. In order to create a desired thrust profile [2], the only geometrical parameters which can be changed are:
40 • Length Chapter 3 –Propulsion design • Outer diameter of the grain • Inner diameter of the grain. • Exposed and inhibited surfaces.
Figure 3.2: the parameters available for grain design
In order to reduce the exposed surface area, the outer area of the grain is inhibited by a cardboard tube, known as the inhibiter. During casting, the sorbitol is absorbed by the cardboard. The potassium nitrate of the propellant is not absorbed by the inhibiter. This property enables a good joint between the two materials and reducing the flammability of the inhibiter.
Since the geometry of the grain depends on the desired thrust profile, the only option to produce a motor with more propellant is to increase the number of grains and separate them
Mark Uitendaal B.Sc. M.Sc. Thesis
by spacer rings in order to maximize the exposed surface of the grain. This grain configuration is called a BATES grain [2].
Since the density of the propellant is fixed, a motor needs to have a high volume loading fraction in order to maximize the propellant mass. The volume fraction is limited by the core diameter of the grains. The core diameter of this motor should be high in order to maximize the initial mass flow. 41
design Propulsion
- Chapter3
. M.Sc. Thesis Mark Uitendaal B.Sc.
3.3.1 Thrust profile
Following from the requirements for the booster motor, specific thrust profile requirements can be derived:
42 • Rapid thrust-up Chapter 3 –Propulsion design • High initial thrust levels • Total impulse estimation of about 4500 Ns.
The motor should have a small thrust-up time, because high initial accelerations are desired to maximise the tower exit velocity.
The thrust levels of the boosters should be high in order to maximise the staging velocity.
Initial calculations showed the total impulse of the booster stage should be in the range of 18 to 20 KNs. Since a quad motor configuration was chosen in the initial design the total impulse per motor should be in the range of 4500 to 5000 Ns.
The specific impulse of the boostermotor was estimated on about 110 sec, which corresponds to an effective exhaust velocity of about 1080 m/s. The total effective mass of propellant in the motor can now be estimated to about 4.2 kilos.
In order to achieve the desired thrust profile a grain configuration was designed as a slightly regressive profile. The thermal loads on the motor will be highest in the end of the motor burn. This will lead to a lower casing burst pressure at the end of the burn compared to the beginning. The regressive profile enables high initial thrust and pressure, thereby limiting material stresses near the end of the burn, enabling a more efficient design.
To maximize the propellant volume contained within the motor, a top grain is added to the BATES configuration
The top grain, which is referred to the “start assist grain” is has several functions
• Assisting the ignition of the motor. This grain will create a flux of very hot particles, which are pushed through the core of the motor, thereby igniting the exposed uninhibited surfaces of the grain.
• Reducing the heatflux to the endcap. By reducing the heat load towards the encap this part can be made out of lighter material, improving overall mass ratio of the motor of the motor.
A BATES configuration of 8 cylindrical grains together with one end burner were selected
In order to calculate the operating pressure of the booster motor a special motor designtool was made, which can predict motor pressure and performance. A detailed description of the simulation is explored more in detail in chapter 4 - Simulations.
Predicted pressure of the booster motor was simulated via the MATLAB Motor simulation tool MPPT as described in section 4.2.
Mark Uitendaal B.Sc. M.Sc. Thesis
43
design Propulsion
- Chapter3
Figure 3.3: simulated pressure of the booster motor
With this simulated pressure, which originated via the klemmung 2 and mass balance in the simulation, another important rocket design parameter can be obtained, the thrust.
Figure 3.4 simulated thrust of the booster motor
2 For klemmung, see chapter 4 - Simulations
. M.Sc. Thesis Mark Uitendaal B.Sc.
3.3.2 The design of the booster motor
The casing of the boostermotor is constructed out of Glass-fibre composite wrapped around a thermal liner made out of brown coloured PVC. The dark colour of the thermal liner was chosen in such way that the casing was shielded from infrared radiation. 44 • The top four grains are coated with a special pyrotechnic lacquer made out of Chapter 3 –Propulsion design nitrocellulose and fine grinded blackpowder. This ensures rapid ignition of the top grains.
Figure 3.5: a sliced view of the boostermotor, depicting all important components.
• The nozzle: the nozzle in a solid rocket motor is not only for generating thrust, but also to sustain the chemical reaction in the motor by regulating the pressure in the motor. The nozzle is made out of construction steel, which can be manufactured easily and cheaply. The nozzle has two O-ring grooves in order to perform a gas seal between the nozzle and the casing.
• The endcap: the boostermotor is sealed by the endcap, which is also sealed by two O- rings. The endcap is made out aluminium in order reduce construction mass. The endcap has a threaded hole in order to attach the motor retainer bolt to it.
Mark Uitendaal B.Sc. M.Sc. Thesis
• The two retainer rings: are the parts which transfer the load of nozzle and endcap to the casing. The retainer ring is made out of 2024 aluminium.
• The casing: the casing is the pressure vessel of the motor. For the booster motor only 1.5 mm glass fibre was selected because of cost restrictions.
45 • The thermal liner: in order to protect the casing of the motor against thermal stresses a thermal liner was selected. The thermal liner is made out of commercial quality Poly Vinyl Chloride (PVC). This part limits the diameter options, because it is only sold in
specified diameters. design
• The retainer bolts: in the ring transfer the stress from the retainer rings through the thermal liner to the composite casing. The retainer bolts are only loaded in the shear Propulsion
direction. The bolts used in the boostermotor are standard quality M5 bolts. The bolts - are placed 25 mm from the edge of the casing in order to prevent stress concentrations in the casing.
The nozzle and the endcap are attached to the casing by a retainer ring, which is connected to Chapter3 the casing by 4 bolts. All forces acting on the nozzle are transferred to the retainer ring. The defined plane of the retainer-ring is installed perpendicular to the centreline of the motor, ensuring the centreline of the motor to be aligned with the centreline of the motor.
The O-ring grooves keep the O rings into place. The double O-rings provide an excellent gas- seal between the casing and the nozzle, ensuring no leakages and nozzle blow by [2].
Figure 3.6: the retainer ring assembly locks the nozzle into place.
. M.Sc. Thesis Mark Uitendaal B.Sc.
3.4 The upper stage motor design:
The motor which propels the second stage of the Stratos vehicle has more than one function:
46 • To provide propulsion
Chapter 3 –Propulsion design • To provide aerodynamic stability of the second stage
• To transfer flight stresses through the vehicle in when in the two stage configuration.
The upper stage motor is part of the load carrying structure of the vehicle. The fins of the upper stage of the vehicle are connected directly to the motor casing via a fillet connection and glass fibre tip to tip reinforcement [2]
The capsule section is connected to the second stage motor at the front skirt of the motor.
3.4.1 The thrust profile
The requirements for the thrust profile of the upper stage motor were identified as:
• Neutral or quasi neutral thrust profile • Smoke grain, which will need to operate till apogee • Total impulse of about 15000 Ns.
The smoke grain produces an amount of gas which fills the wake of the rocket. This gas- emission will reduce the pressure drag in the coasting phase. The reduction of coasting drag will enable a higher apogee altitude.
In order to satisfy the total impulse requirement the total amount of propellant mass was set at 12.5 Kg of propellant. This amount of propellant can be divided into several grain geometries.
The motor simulation program was used in order to simulate different BATES grain configurations in order create the most neutral profile. The option selected for the upper stage motor was a 7 grains BATES configuration of about 1.8 kg per grain.
In order to calculate the operating pressure of the upper stage motor a special motor designtool MPPT was made, which can predict motor pressure and performance. A detailed description of the simulation is explored more in detail in chapter 4 - Simulations
Mark Uitendaal B.Sc. M.Sc. Thesis
47
design Propulsion
- Chapter3
Figure 3.7: the simulated operating pressure of the upper stage motor
Figure 3.8: the simulated thrust of the upper stage motor
. M.Sc. Thesis Mark Uitendaal B.Sc.
3.4.2 The igniter
The motor is used as a second stage motor; therefore this places some requirements on the ignition of the motor. The igniter must withstand acceleration in positive direction during boosting and negative direction during coasting. The igniter needs to ignite the motor with a 48 static pressure lower than air pressure at sea level. The total length of the propellant grain is
Chapter 3 –Propulsion design about 1.5 metres, in order to reliable ignite the total exposed area the igniter must produce a flux of heated gas of the same magnitude.
The igniter selected to satisfy the requirements is the pyrogen igniter. This type of igniter is essential a small rocket motor which ignites the grain by shooting a flux of heated gasses through the core of the grain.
The pyrogen igniter is an EED and is explored more in the section 2.6 - pyrotechnics
Mark Uitendaal B.Sc. M.Sc. Thesis
3.4.3 Design of the upper stage motor
49
design Propulsion
- Chapter3
Figure 3.9: a sliced view of the upper stage motor, depicting all important components
The casing of the upper stage motor is constructed out of carbon fibre. This material was chosen because of its extremely high specific stiffness and strength.
In order to protect the casing against thermal loads, a thermal liner made out of PVC was selected.
The nozzle for the upper stage motor is a so called “Zeta-nozzle” a nozzle with a half divergence angle. The nozzle has a higher C f, creating a higher overall efficiency, but is harder to produce. The lower divergence angle is the result of the geometrical constrains with the interstage coupler. The nozzle is made out of construction steel and is intended for usage multiple times. A twofold O-ring groove provides the seal between the nozzle and the casing.
The aft skirt of the motor is the connection between the upper stage and the interstage coupler. The aft skirt is made out of aluminium inner busher tube, reinforced with carbon fibre.
The retainer ring transfers the load from the nozzle or endcap to retainerbolts.
The four retainer bolts transfer the loads from the retainer ring to the casing. The aft retainer bolts are covered by the fillet of the fins. The frontal retainer bolts are in free stream airflow. The bolts are commercial M10 bolts.
The propellant grains are dimensioned such that the total mass of a grain won’t exceed the 2 kg maximum per grain which is a transport requirement.
. M.Sc. Thesis Mark Uitendaal B.Sc.
Since the motor is ignited in flight, a pyrogen igniter is used. This type of igniter is basically a small rocket motor which shoots a flame through the ports of the grains.
To reduce the pressure drag during coasting a smoke grain is added to the motor. This grain will fill up the wake of the vehicle while travelling in an unpowered configuration.
50 In order to connect the motor to the capsule section a special forward skirt was constructed.
Chapter 3 –Propulsion design The forward skirt provides stiffness to the whole rocket and can be connected to the capsule section of the vehicle via a sliding lap joint of 300 mm. .
Mark Uitendaal B.Sc. M.Sc. Thesis
During the design of the Stratos rocket, accurate performance predictions of the rocket and the motors proved to be invaluable information. 51
4.1 The simulation software
In order to predict performance in rocket flight and motor performance, a simulation program imulation S
© - is written in MATLAB . The simulation package consists of two elements:
• Motor performance prediction program • Flight trajectory prediction program 4 Chapter
The motor performance prediction program , which is not only used to predict the performance of several grain configurations. The program also aids in the design process by calculating the klemmung and operating pressure of the motor. The program cooperates together with the flight trajectory prediction program by writing motor output files, which can be imported by the flight trajectory prediction program. This program is named the Motor Performance Prediction Tool or MPPT.
A flight trajectory prediction program , is a simulation program which is used to predict important flight trajectory parameters such as: apogee altitude, velocity, Mach number and range. The program uses rocket design inputs, aerodynamic data from the AEROLAB program, a detailed model from the atmosphere and motor output files from the motor performance prediction program or actual motor data from static firings. This program is named the Flight Trajectory Prediction Tool or FTPT.
The two programs are described in detail in the following two chapters, dealing with the assumptions, the basics models and the simulation program. The results of the simulation are compared with tests in chapter 6 – Flight and data analysis.
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.2 The motor performance prediction program
An accurate motor simulation program can be very helpful to simulate accurate motor performance for testing and altitude predictions. This program, programmed in MATLAB is based on the geometrical shape change of the grains, which alter during the whole burn time. 52 The motor performance program is constructed in such way that it can communicate with the Chapter-Simulation 4 flight simulation program. The motor prediction program operates by having a geometrical mesh as the web thickness of the grain. The web thickness of the grain is defined as the thickness between the inner and outer diameter of the grain.
Figure 4.1: the nomenclature of the grain
It can be seen that the web thickness is defined as Equation 4.1.
t = r − r 2 1 Equation 4.1
Where: • t = webthickness [mm] • r2 = the outer radius of the grain [mm] • r1 = the inner radius of the grain [mm]
Mark Uitendaal B.Sc. M.Sc. Thesis
The program works in four steps:
• Klemmung calculation • Gas production and pressure calculation • Thrust calculation • Re-sampling 53
All four steps, including the valid equations are dealt with in the following four chapters.
The klemmung calculation begins with a geometrical mesh and calculates the klemmung, and the free casing volume of the motor. imulation S -
The gas production and pressure calculation uses the klemmung and free casing volume.
The thrust calculation uses the pressure to calculate the thrust of the motor. 4 Chapter The re-sampling is necessary since the flight simulation program works on a time based mesh of 100 Hz. This implies that the motor simulation program needs to resample the output data to a 100 Hz. data stream, which can be handled by flight simulation.
All integration methods just use first order numerical procedures, sometimes referred to as the Euler intergration method.
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.2.1 Klemmung calculation
For pressure and performance calculations the klemmung , the grain volume and the grain mass must be known for each simulation step. This calculation process is depicted in Figure 4.2.
54 Chapter-Simulation 4
Figure 4.2: a flowchart for calculating some grain properties
The klemmung [7] of a solid rocket motor is defined as:
A Kn = burning A* Equation 4.2
* Where the A burning is the total burning surface of the motor grain. The A is the nozzle throat area.
Figure 4.3: the nozzle throat area in the booster motor nozzle
Mark Uitendaal B.Sc. M.Sc. Thesis
The burning surface of a single Bates grain is inhibited on the outside of the grain
55
imulation S -
Chapter 4 Chapter
Figure 4.4: the exposed surface on the grain.
The exposed burning surface can be calculated via:
A = π ⋅ r 2 − r 2 + ⋅ r ⋅π ⋅ h burning ( outer inner ) 2 inner 1 Equation 4.3
Where router and rinner are the outer diameter and core diameter of the grain respectively. The variable h1 is the length of a single grain.
In the top of the motor a start-assisting grain is placed. This grain is a so called “cigarette- burner” or “end-burner”. The burning surface of this grain can be calculated by:
2 Aburning = π ⋅ router Equation 4.4
The throat area A* is assumed not to change over time. This assumption is made based on the selection of materials. The throat area A* can be calculated with:
* 2 A = π ⋅ rthroat Equation 4.5
The propellant volume of a single hollow tube grain can be calculated from the geometrical data of the grain:
V = π ⋅ r 2 − r 2 ⋅ h grain ( outer inner ) 1 Equation 4.6
The start-assisting grain volume can be calculated from:
. M.Sc. Thesis Mark Uitendaal B.Sc.
V = π ⋅ r 2 ⋅ h grain outer 2 Equation 4.7
Where h2 is the length of the start start-assisting grain
56 The empty casing volume can be calculated via:
Chapter-Simulation 4 V = π ⋅ r 2 ⋅l ca sin g inner inner Equation 4.8
Where linner is the inner length and rinner is the inner diameter of the casing, defined between the fronts of the convergent part of the nozzle, to the end cap.
In order to simulate the grain getting smaller, some functions are applied to it geometrical shape:
r = r − ∆x 1 1 initial Equation 4.9 h = h − ∆x 1 1 int ital 2 Equation 4.10 h = h − ∆x 2 2 initial Equation 4.11
These functions represent the grain regression characteristics
Figure 4.5: the regression of the grain in the simulation
Where of course the total volume of propellant is calculated as:
Mark Uitendaal B.Sc. M.Sc. Thesis
N V = V propellant ∑ grain 1 Equation 4.12
And the total burning area with: N A = A 57 propellant ∑ burning
1 Equation 4.13
Where N is the total amount of grains. imulation
S -
Chapter 4 Chapter
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.2.2 Gas production and pressure calculations In order to calculate the pressure, and to predict motor thrust, a gas production, a mass balance and pressure calculation will have to be made. The pressure calculation mechanism is depicted in Figure 4.6, a detailed overview of the mass balance can be seen in Figure 4.7. 58 Chapter-Simulation 4
Figure 4.6: the pressure calculation via the mass balance
Figure 4.7: the mass balance
In order to calculate the density of the exhaust products, the free volume in the casing will have to be calculated.
The free volume in the casing, which is available for exhaust products, can be calculated via: V = V −V free ca sin g grains Equation 4.14
In order to calculate the density of the reaction products in the motor casing, the mass of the reaction product will have to be known. First, the mass flow per geometrical step generated by the propellant grain is calculated via:
Mark Uitendaal B.Sc. M.Sc. Thesis
m = m − m x x+1 Equation 4.15
Where mx is the instantaneous mass of the propellant grain:
59 mx = Vx ⋅ ρ propellant ⋅ηcast
Equation 4.16
Where ηcast is the casting quality. Depending on the test sample produced from the same propellant batch, this parameter is about 0.9 to 0.94. imulation S -
The mass flow per second which is leaving the motor casing through the nozzle can be calculated via Equation 4.17 [7]. This of course with the assumption that the nozzle is chocked, therefore it is referred to as the critical mass flow. 4 Chapter τ ⋅ (P − P ) ⋅ A* m = chamber 0 & nozzle R ⋅Tc ⋅η combustion Equation 4.17
In case of the simulation, the nozzle is closed until the critical mass-flow is reached.
Where the τ is called the Vanderkerckhoven constant, which is specified as:
γ +1 2 2⋅()γ −1 τ = γ ⋅ 1+ γ Equation 4.18
Since the mass flow through the nozzle is specified in [Kg/s] and the mass flow generated by the propellant grain is specified in [Kg/step], it is necessary to determine the regression-rate of the grain. The regression rate without erosive burning can be calculated via De Vieille law:
r = a ⋅ P n Equation 4.19
Where a and n are defined as the burn rate and pressure-exponent of the propellant. In case of the simulation this is 5.5 and -0.013 respectively [2].
Due to the higher gas velocity in the cores of the grain in the initial state of the motor burn, some erosive burning is expected. Erosive burning implies a higher regression rate [2]
Since Equation 4.19 doesn’t contain any effect of erosive burning a modified version of the “De Vieille burning law” is used:
n r = 1( + Cerosive ⋅ G) ⋅ a ⋅ P Equation 4.20
Where Cerosive is a constant. This constant is set at 0.1, implying a 10% of the grain surface to have a higher than nominal regression rate. G is expressed as:
. M.Sc. Thesis Mark Uitendaal B.Sc.
r 2 G = λ − inner treshold 2 rthroat Equation 4.21
60 Where λtreshold is a constant after which port/throat ratio the erosive burning doesn’t occur. In
Chapter-Simulation 4 the simulation this is set at 6. This value is chosen such that the gas velocity is such that erosive burning doesn’t occur.
With Equation 4.20, the regression rate can be calculated, so the time per geometrical step size can be calculated with:
∆x ∆t = r Equation 4.22
By combining Equation 4.17 and Equation 4.22, a mass balance can be set up via:
n+1 m = m − m ⋅ ∆t stored ∑ generated & nozzle n Equation 4.23
By combining Equation 4.14 and Equation 4.23, the density of the reaction product can be calculated with:
mstored ρrp = V free Equation 4.24
Another important parameter is the C*, or ideal characteristic exhaust velocity which is calculated with:
* 1 C = Tc ⋅ R τ Equation 4.25
Since now the klemmung and the density of the reaction-products are known, the pressure P in the motor casing can be calculated with:
1 * 1−n Pchamber = (Kn ⋅ ρ rp ⋅ C ) Equation 4.26
Where n is the pressure exponent of the propellant, which is defined as -0.013.
Mark Uitendaal B.Sc. M.Sc. Thesis
4.2.3 Thrust calculation
The thrust production of the nozzle, including the total impulse calculation is depicted in Figure 4.8. The chamber pressure per step, the nozzle geometry and the initial propellant mass needs to present in order to calculate all desired values. 61
imulation S -
Chapter 4 Chapter
Figure 4.8: the thrust production by the nozzle.
With Equation 4.26 it is now possible to determine the pressure in the combustion-chamber.
The thrust can now be calculated via the C f of the nozzle which is defined as:
γ −1 γ 2γ Pe Pe Pa Ae C f = τ 1− + − ⋅ γ − P P P A* 1 c c c Equation 4.27
In which:
τ = Vanderkerckhoven constant [-] γ = ratio of specific heats [-]
Pe = the pressure at the exit plane of the nozzle [Pa] Pc = the pressure in the combustion chamber [Pa] Pa = the ambient pressure [Pa] 2 Ae = the cross-sectional area of the exit plane of the nozzle [m ] A* = the cross-sectional area of the nozzle throat [m2]
With the help of Equation 4.5, Equation 4.26 and Equation 4.27, the motor thrust [N] can be calculated via:
* F = C f ⋅η nozzle ⋅ Pchamber ⋅ A Equation 4.28
. M.Sc. Thesis Mark Uitendaal B.Sc.
Since the thrust is now known, the total impulse can be calculated with
tb I = ∫ F ⋅ dt 0 Equation 4.29 62
Chapter-Simulation 4 The total impulse is an important parameter of a solid rocket motor, since it represents the total amount of energy contained in the motor. An other important parameter of the motor is
the specific impulse (I sp ). The specific impulse is a very important parameter in a rocket since it directly correlates with the velocity of the gasses expelled from the nozzle Equation 2.1.
The I sp directly correlates with the burnout velocity of the vehicle.
With Equation 4.29 the specific impulse now can be calculated via:
I I = sp m ⋅ g o 0 Equation 4.30
Where:
• Isp = the specific impulse of the propellant • I = total impulse of the motor • m0 = the initial mass of propellant in the motor • 2 g0 = gravitational acceleration at sea level (9.80665 m/s ).
The simulation itself represents an ideal situation, with an instantaneous ignition of all exposed burning surfaces. In reality this is not the case, and only a partial ignition of the exposed grain surface will occur. In order to simulate a partial ignition of the grain, and representative start-up behaviour of the motor, Equation 4.31 is applied to the geometric variables.
−t⋅c ζ start = η startup + 1( −η startup ) ⋅ 1( − e ) Equation 4.31
The value ηstartup represents the ratio of the grain which is instantaneous ignited. The t and the c are variables in order to simulate the start-up behaviour during the first part of the motor burn. Where t is the time till full pressure and c a constant which is set as 5. This value was chosen in order to the 1− e−t⋅c term to at approximately 99.99 % after the first 1000 steps, which shows a best fit in the start-up behaviour of the motor tests.
Mark Uitendaal B.Sc. M.Sc. Thesis
63
imulation S -
Chapter 4 Chapter
Figure 4.9: simulated start-up behaviour via an exponential function
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.2.4 Re-sampling
The motor simulation has not a fixed time mesh, because it uses an equidistant geometrical mesh. The motor data needs to be compiled into a special format in order to enable the flight trajectory simulation program FTPT to use it. 64
Chapter-Simulation 4 The data output file of the motor program contains:
• Motor casing mass • Thrust profile with an 100 Hz. sampling rate • Propellant mass profile with an 100 Hz. sampling rate • Burn time of the motor
The re-sampling of the thrust profile is done via interpolation, giving a time stamp on each interpolated entry.
Figure 4.10: the re-sampling by interpolation in order to gain a fixed timestamp in the output file
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3 The flight simulation program
The flight simulation is used for several options:
• Rocket design evaluation 65 •
Flight parameter optimization • Failure scenario predictions • In situ flight trajectory predictions
imulation S
Rocket design evaluation:, in order to have an almost instantaneous prediction on the design - changes, the simulation can be used. In the conceptual design trade off phase this tool was extensively used.
Flight parameter optimization: some parameters in flight can be optimized, such as launcher 4 Chapter settings (elevation angle, compared to the wind speed) and the drift time between the two stages. These parameters can be optimized by iteration.
Failure scenario prediction: for some scenarios the simulation can be used to simulate other than nominal flight trajectories. Scenarios as single booster motor misfires, failure of stage separation, thrust misalignment, thrust difference or premature second stage ignition.
In site flight trajectory predictions: this can assist in recovery of the vehicle by predicting the impact point of the vehicle. 4.3.1 Assumptions of the simulation
In order to simplify the simulation, some basic assumptions are made in the simulation environment and rocket designs.
The flight trajectory prediction program is based on several assumptions:
• Flat earth • Small angles of attack, so linearization holds • Constant gravitational field • Flight through the troposphere and tropopause. • No rotation allowed in the tower • Frictionless lugs in the launch rail • Completely rotational symmetric rocket • No thrust during coast phase (including smoke grain burn) • Drag coefficient of powered vehicle when activating the smoke grain • A constant sampling frequency is used, which is the same as the post-sampling frequency of the motor simulations • The ignition characteristics of the second stage motor are the at ignition altitude the same as on sea level.
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.2 Input data for the flight simulation program
The program needs several input data in order to predict a flight. These input data can be divided into four branches:
66 • Rocket data Chapter-Simulation 4 • Motor data • Weather or environmental data • Other data
The rocket data : this data consists of geometrical data such as length and diameter, mass data and aerodynamic data. This data is used centre of gravity and inertia predictions.
Motor data: such as thrust data and casing mass data. This data is used for propulsion and inertia predictions.
Weather data : defines the atmosphere which the rocket is travelling through.
Other data: This is secondary data, which is needed to complete the simulation and make accurate predictions
Figure 4.11: an overview of the input data necessary for the flight simulation program.
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.3 The rocket geometrical parameters
The rocket has some specific geometrical properties which are different in each rocket configuration. The geometrical properties determine the outer shape of the vehicle and thus the outer shape and wetted area of the vehicle. The aerodynamic properties of the vehicle can derived from the outer shape in combination with the speed regime. 67
For the Stratos vehicle two model configurations are identified, both with different aerodynamic, geometric, mass and inertia properties. The two model configurations are:
imulation S
• - Two stage model, which is valid when the booster stage is attached to the main stage • Single stage model, which is valid after booster stage separation Chapter 4 Chapter
Figure 4.12: the two model configurations possibilities for the Stratos vehicle
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.4 Aerodynamic parameters.
The aerodynamic properties of the vehicle are calculated via AEROLAB, an aerodynamic rocket prediction program by Hans Olav Toft, of the Danish Amateur Rocket Klub or DARK. 68
Chapter-Simulation 4 All aerodynamic parameters predicted by AEROLAB are converted to non dimensional
parameters via the nominal reference area A ref which can be seen in Figure 4.13
Figure 4.13: The cross-sectional area of the rocket is the aerodynamic reference area
The booster of the Stratos has a different cross-sectional area than the second stage, therefore the reference area will change during booster separation. Also the diameter of the model is different,
The AEROLAB program calculates 3 aerodynamic parameters from the basic aerodynamic outline of the rocket.
• The drag coefficient C d • The lift curve slope coefficient C lα • The location of the centre of pressure X cp .
The drag coefficient (c d) differs in each rocket configuration, Mach number and the fact that the rocket is expelling gas out of the nozzle or not (the state of the motor).
The drag coefficient c d is dependant on the mean relative skin roughness of the wetted area of the vehicle. This is an empirical value which is extremely hard to estimate in the design stage. According to the literature study [1] several values are relevant:
Skin roughness: remarks:
• 0.0001 – 0.0005 mm Absolute smooth • 0.0006 – 0.0017 mm Polished metal or wood • 0.0018 – 0.0040 mm Natural sheet metal • 0.0040 – 0.0095 mm Carefully painted • 0.0096 – 0.0680 mm Painted • 0.0681 – 0.6000 mm Rough metal
The vehicle was considered completely smooth, but several protrusions were identified in the beginning of the design process. Examples of these protrusions are: Safe/arm plugs, bolted connection and communication and breakwire connections. For that reason the relative skin
Mark Uitendaal B.Sc. M.Sc. Thesis
roughness of the Stratos vehicle was selected as 0.068 mm, which is considered as a painted surface, although the quality of the paintwork was considered “carefully painted”.
The lift-slope coefficient (C lα) differs in each aerodynamic configuration and depends the aerodynamic shape and on the Mach number. The lift slope coefficient is calculated around an zero angle of attack situation, which is the case in nominal flight conditions. The flight surfaces of the vehicle will stall at high angles of attack; therefore the angle of attack in the 69 simulation is limited to a preset maximum.
The location of the centre of pressure of the rocket ( X Cp ) This location is measured from the tip of the
nosecone and depends on the aerodynamic shape as well as the Mach number. imulation S
-
4 Chapter
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.5 Instantaneous mass of the model.
The mass and the position of gravity have a big effect on the performance and the stability of the vehicle. The parameters will not be the same during every phase of the flight. This 70 phenomenon is caused by two things: Chapter-Simulation 4 • Mass expelled during the powered phases of flight in the form of exhaust products.
• Separation of components: The expelled booster and all its construction mass is separated from the rest of the rocket after booster burnout.
The gas expelled by the rocket motors is modelled after the assumption that the nozzle exit velocity is constant, and the nozzle is always in a chocked condition. The mass flow in kg/s can than be modelled as:
Tactual m& = tb T ⋅ dt ∫ g ⋅ 0 0 M ⋅ g 0 Equation 4.32
The mass flow per second is necessary in order to simulate the jet-damping of the rocket. The jet damping is a parameter in stability which is explored in Equation 4.58. The instantaneous mass of the vehicle per step can now be calculated by Equation 4.32, by multiplying this by the time step size and subtracting this from the total mass.
The mass flow per simulation step can than be modelled as:
m = m ⋅ dt & step & Equation 4.33
The mass distribution of the rocket is modelled as three parts:
Figure 4.14: the Stratos vehicle divided into three sections, each modelled as a point mass.
Mark Uitendaal B.Sc. M.Sc. Thesis
• Section I: the capsule section. This mass will not change during flight, so the mass of this section is modelled a constant mass:
m = m sec ton I capsule Equation 4.34 71
• Section II: The sustainer section, which mass is variable during the second powered phase.
m = m + m − m imulation
sec tion II ca sin g propellant & step S - Equation 4.35
• Section III: The booster section. The mass of this section is variable because of mass
flow and component separation. 4 Chapter
m = m + m − m sec tion III ca sin g propellant & step With: m = sec tion III 0 when the booster is separated from the rocket
Equation 4.36
By combining Equation 4.33, Equation 4.34, Equation 4.35 and Equation 4.36 the instantaneous mass as used in the flight simulation of the vehicle can be modelled as:
3 m = m ∑ component 1 Equation 4.37
With Equation 4.37 it is now possible to calculate the instantaneous mass per step in the simulation. The vehicle was modelled as three sections, which can be seen in Figure 4.14. The position of the centre of gravity can now be calculated with Equation 4.38.
(X cg ) ⋅ m tion I + (X cg ) ⋅ m tion II + (X cg ) ⋅ m tion III 1 sec 2 sec 3 sec X cg = m Equation 4.38
Where all the positions are from common reference point at the tip of the nosecone [mm].
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.5 Moment of inertia model
In order to determine the rotation of the vehicle, the inertia of the vehicle needs to be modelled. The inertia of an object is the resistance of an object to rotation. The inertia model is the most important during situations in flight where the rotational acceleration of the 72 vehicle is high, such as tower exit and drifting. In order to have a good overview of the Chapter-Simulation 4 limitations of the model used in the flight trajectory simulation program, a list of assumptions is stated:
The inertia model is constructed with the following assumptions and simplifications:
• The mass of the fins are very small in combination with the rest of the rocket body, therefore the influence on the inertia and mass are discarded.
• The mass flow of all the booster motors is the same.
• The mass distribution is homogeneous within a section.
• The geometric shape of the booster is modelled as a cylindrical shape, which is actually a very complex geometric shape of 4 cylinders and a conical section.
• The geometrical shape of the nosecone is modelled as an conical section instead of in parabolic section.
The inertia model also consists of the same three parts as the mass model. The inertia of one section is composed of two parts:
• The inertia of the part, depending on the shape of the part.
• The Steiner translation [9] between the part and the centre of gravity of the total vehicle. This is can be seen in Equation 4.39.
2 I steiner = mcomponent ⋅ rcg Equation 4.39
Mark Uitendaal B.Sc. M.Sc. Thesis
Section I: the capsule section. This section is modelled as a conical object with a specific mass. This mass will not change during flight. The inertia of this section is modelled as:
73
imulation S -
Figure 4.15: the capsule section is modelled as a conical section
Chapter 4 Chapter 3 2 3 2 2 I xx = m tion I ⋅ r + m tion I ⋅ l + m tion I ⋅ (X cg − X cg −component ) 20 sec 5 sec sec
Equation 4.40
Section II: The sustainer section. This section is modelled as a cylinder and has a variable mass because of the gasses expelled during burning.
Figure 4.16: the sustainer section is modelled as a cylindrical section
1 2 1 2 2 I xx = m tion II ⋅ r + m tion II ⋅l + m tion II ⋅ (X cg − X cg −component ) 4 sec 12 sec sec
Equation 4.41
. M.Sc. Thesis Mark Uitendaal B.Sc.
Section III: The booster section. This section is also modelled as a cylinder, only with a bigger radius. The mass of this section is variable because of mass flow and component separation.
74 Chapter-Simulation 4
Figure 4.17: the boostersection is modelled as a cylindrical section
1 2 1 2 2 I xx = m tion III ⋅ r + m tion III ⋅l + m tion III ⋅ (X cg − X cg −component ) 4 sec 12 sec sec
Equation 4.42
The model is depicted in Figure 4.18:
Figure 4.18: The inertia model build up out of the three sections
Mark Uitendaal B.Sc. M.Sc. Thesis
The total inertia model depends on the position of the centre of gravity within the total vehicle. Since the Steiner translation of each part is already calculated at each component calculation, the total moment of inertia of the vehicle can be calculated via a summation, such as Equation 4.43.
i I = ()I xx ∑ xx component 75 0 Equation 4.43
The centre of gravity of the vehicle shifts during operation of the motors, because of mass flow out of the nozzle. Due to this phenomenon, the inertia of the vehicle will change during imulation S - the motor burns of the two stages. During the jettisoning of the spend booster stage, the mass of section III is changed to zero. This creates a large shift in mass distribution, centre of gravity and moment of inertia. Chapter 4 Chapter
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.6 The weather model
In order to have an accurate flight prediction, several parameters of the simulation environment are needed: 76
Chapter-Simulation 4 • Wind velocity • Air pressure • Temperature
All parameters are variable in altitude, therefore must be specified at different altitudes.
The last two parameters can be calculated as if the vehicle would fly in the International Standard Atmosphere (ISA). Since the launch conditions at Esrange could differ from ISA, a special program was made in order to define the environment from measured points, enabling atmospheric balloon measurements when the rocket campaign would be in progress.
The temperature, pressure and wind conditions at certain altitudes can be imported in the flight simulation via a special import program. These measurements can be imported via a ISA table [8] or from weather balloons from the local launch site.
Via linear interpolation of the actual temperature, pressure and wind on the current altitude are calculated.
With the temperature and pressure following properties can be calculated via Equation 4.44 and Equation 4.45.
From the temperature a pressure distribution throughout the atmosphere, the density and media propagation speed can be calculated on every specified altitude along the rocket trajectory.
Density: the density can be calculated via the equation of state:
P ρ = Rgas ⋅T Equation 4.44
Propagation speed: the speed of sound, which is necessary for the calculation of the Mach number, can be calculated with:
Vsound = γ ⋅ Rgas ⋅T Equation 4.45
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.7 The reference frames
In order to simulate a dynamic situation, first some reference frame and angles needs to be defined. Two reference frames can be defined in a two dimensional rocket flight trajectory:
• Body fixed reference system 77 • Inertial reference frame.
The rocket itself has an own coordination system which is explained in Figure 4.19:
imulation S -
Chapter 4 Chapter
Figure 4.19: The coordination systems within the flight simulation of the rocket.
The angle θ is the angle between the inertial reference frame and the body fixed reference frame. The angle α between the local airflow and the body fixed reference frame, representing the angle of attack of the vehicle.
The transformation from the inertial reference frame to the body reference frame is done via matrix:
cos θ sin θ 0 T = − θ θ bi sin cos 0 0 0 1 Equation 4.46
. M.Sc. Thesis Mark Uitendaal B.Sc.
The transformation from the aerodynamic reference frame to the body reference frame is done via matrix:
cos α − sin α 0 T = α α ba sin cos 0 78 0 0 1
Chapter-Simulation 4 Equation 4.47
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.8 Forces on the rocket
When an external force is applied to the rocket body it will accelerate to the opposite side. The internal and external forces which are be applied in the two dimensional simulation are:
79 • Thrust (only in a powered phase) • Weight • Drag • Lift imulation
S - Thrust : the motor in the rocket will produce thrust. This thrust is directly imported from the motor simulation. The thrust is corrected for altitude by taking in account the pressure difference with sealevel. This done via Equation 4.48. The nozzle exit pressure is set at a
constant pressure, which is the mean value of the nozzle exit pressure during its operation. 4 Chapter
T = m ⋅Ve + A ⋅ P − P & e ( e a ) Equation 4.48
The weight of the vehicle is mass of the rocket multiplied by the gravitational parameter
w = m ⋅ g 0 Equation 4.49
Drag : the rocket will experience drag due to the air friction
D = 1 ⋅ ρ ⋅ V 2 ⋅ A ⋅ c 2 ref d Equation 4.50
The value of cd is dependant on the rocket configuration, the state of the motor, as well as the Mach number. The drag is always parallel, but in the opposite direction with the airflow.
Lift : due to an angle of attack the whole rocket body will produce lift
L = 1 ⋅ ρ ⋅ V 2 ⋅ A ⋅ c 2 ref l Equation 4.51
The value of cl is dependant on the rocket configuration, the angle of attack as well as the Mach number. The lift is always orthogonal on the airflow.
Since the cl value is dependant on the angle of attack, the following linearized relation is introduced: c = C ⋅α l l α Equation 4.52
. M.Sc. Thesis Mark Uitendaal B.Sc.
All the forces on the rocket are illustrated in Figure 4.18, note the direction of the forces.
80 Chapter-Simulation 4
Figure 4.20: The forces on the rocket body during powered flight
The thrust [T] is aligned in the centreline of the body. The weight [W] vector is pointing straight down in the inertial reference frame, which conversion matrix is stated in Equation 4.46. The lift and drag of the vehicle are specified in the aerodynamic reference frame, which conversion matrix is calculated in Equation 4.47. The forces in the body reference frame can now be calculated as follows:
L 0 0 F = T ′ ⋅ − D + T ⋅ −W + T b ab bi 0 0 0 Equation 4.53
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.9 Rotation
Another equation can be solved in order to determine the flight angle θ and angle of attack α. This can be done with the linearized moment equation around the centre of gravity of the rocket. 81
2 Ω ⋅ d M = ()X − X ⋅ A ⋅ 1 ⋅ ρ ⋅ V ⋅ − C ⋅α − C ⋅ rocket cg cp cg ref corrective damp 2 V Equation 4.54 imulation
S Ω ⋅ d - rocket The term is chosen such that the rotation velocity is dimensionless. V
The corrective and damping coefficients in the moment equation are defined as: 4 Chapter
Ccorrective = Cn α Equation 4.55
The damping of the rocket is performed by two damping mechanisms.
• Aerodynamic damping • Jet damping
Aerodynamic damping is basically the energy bleed off by the drag of rocket out of the rotational movement of the rocket.
Jet damping is the damping moment caused by the mass flow out of the nozzle, which tries counteracting any rotation of the vehicle.
The two damping mechanisms are both responsible for damping any rotational motion as can be seen in Equation 4.56.
Cdamp = Caero + C jet Equation 4.56
In Equation 4.56 the aerodynamic coefficient is defined as:
2 X fin C = Cn ⋅ aero α d 2 Equation 4.57
Where the X fin is the distance between position of the centre of gravity of the rocket and the aerodynamic centre of the fins. Diameter d makes the coefficient is dimensionless.
. M.Sc. Thesis Mark Uitendaal B.Sc.
Where in Equation 4.56 the jet damping coefficient is defined as:
V C = m ⋅ X 2 ⋅ jet & nozzle ()X − X ⋅ A ⋅ 1 ⋅ ρ ⋅V 2 ⋅ d cp cg ref 2 Equation 4.58 82
Chapter-Simulation 4 Where the term X nozzle is the distance between the nozzle and the centre of gravity of the vehicle. V Ω ⋅ drocket Where the term , together with to make the ()X − X ⋅ A ⋅ 1 ⋅ ρ ⋅V 2 ⋅ d V cp cg ref 2 whole jet damping coefficient dimensionless.
Via Equation 4.54 the rotational acceleration can now be calculated via:
M cg Ω& = I rocket Equation 4.59
Via Equation 4.59 the rotational velocity can now be calculated via time integration:
t Ω = ∫ Ω& ⋅ dt 0 Equation 4.60
The flight angle can now be calculated via Equation 4.60:
t θ = ∫ Ω ⋅ dt 0 Equation 4.61
In order to evaluate the damping characteristics and the dynamic behaviour of the rocket the damping ratio can be calculated via:
Cdamp ζ = 2 ⋅ Ccorrective ⋅ I rocket Equation 4.62
Where the damping ratio can have three different cases:
• ς < 0 Negatively damped system, dynamic instability • 0 < ς < 1 Dynamic stability, • ς > 1 dynamic overdamped system
This parameter is used to evaluate the dynamic behaviour of the rocket and investigate the overall stability of the vehicle.
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.10 Acceleration, velocity and position
The body accelerations can be calculated with Equation 4.53 as follows:
F b a b = m 83 Equation 4.63
Where m is the total instantaneous mass of the vehicle as can be calculated via Equation 4.37.
The body accelerations are transformed to the inertial accelerations follows from Equation imulation S -
4.65:
′ a i = T bi ⋅ ab Equation 4.64 Chapter 4 Chapter
′ Where Tbi is transposed matrix of Equation 4.46.
Now the inertial accelerations can be calculated via Equation 4.64, the velocity can be calculated via Equation 4.65:
t V i = ∫ ai ⋅ dt 0 Equation 4.65
It must be noted that the side wind is only one dimensional and is converted to the local wind vector field as Equation 4.66:
Vwind V = T ⋅V + T ⋅ b bi i bi 0 0 Equation 4.66
It must be noted that in the rotation in the tower is constrained by setting Equation 4.55 to 0, thereby excluding the option that the rocket is weather cocking due to side wind while still in the launch tower.
The position in the inertial reference frame is calculated via time integration of Equation 4.66.
t ′ s i = ∫T bi ⋅V b ⋅ dt 0 Equation 4.67
. M.Sc. Thesis Mark Uitendaal B.Sc.
The Mach number of the vehicle, which is of course very important for all aerodynamic properties is calculated via:
V M = Vsound 84 Equation 4.68
Chapter-Simulation 4
Where V sound is calculated by the environment model as shown in Equation 4.45.
4.3.11 Simulation parameters
In order to assure the validity of the simulation, the simulation stops when one of the following requirements is satisfied:
• The angle of attack is higher than a specified maximum • The altitude is lower than a specified minimum • The Mach number is higher than a specified maximum
The angle of attack is higher than its maximum preset value
α ≥ α max Equation 4.69
This angle is limited in order to ensure to bound the linearization error during the simulation
and to set a maximum C l value. The C l value is calculated by Equation 4.52, by a C lα calculated around a zero angle of attack situation. This assumption only holds at small angles of attack.
The altitude of the rocket is lower than ground level.
h ≤ 0 Equation 4.70
Obviously in order to simulate impact into the ground and thereby ending the simulation. This enables the simulation to calculate the ballistic flight-time and the distance between the point of launch and the point of impact.
The Mach number of the vehicle is higher than the preset maximum Mach number:
M ≥ M max Equation 4.71
In order to preserve the integrity of interpolation of the aerodynamic properties. If the Mach number is higher than what the aerodynamic model allows, the interpolation will be an extrapolation, thereby creating possibly a higher estimation error.
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.12 Flight simulation validation
In order to validate the flight simulation software, a comparison was made between the simulations and with the flight of Quick and Dirty on June 1 st 2007. The Quick and Dirty amateur rocket was also a two stage rocket build by Uitendaal en Krancher. [2] The Quick and Dirty rocket was equipped with a flight computer capable of recording accelerations and 85 pressure altitude.
The new aerodynamic model of the Quick and Dirty rocket was also constructed via
AEROLAB. imulation S -
The thrust profile, motor casing mass and rocket booster mass were used from [2], but quality of the data is limited due to the lack of recourses.
Chapter 4 Chapter
Figure 4.21: Comparison between acceleration in simulation (in Cg) and measurement in flight (in Z- Axis)
It can be seen by comparing the acceleration data and the simulated acceleration levels of the simulation are higher (10%) than the actual recorded acceleration data. The measurements in display noise levels of about 15% of the maximum recorded value.
. M.Sc. Thesis Mark Uitendaal B.Sc.
The static air pressure of the Quick and Dirty was recorded by a pressure sensor, which was fed through a static port. The actual position of the static port in combination with the pressure distribution around the vehicle influences the altitude measurements. The altitude is calculated from the static air pressure.
86 Chapter-Simulation 4
Figure 4.22: Comparison between pressure altitude in simulation and measurement in flight
It is must be assumed that the velocity at apogee was almost zero, creating a good and accurate altitude measurement on apogee.
The simulated altitude compared to the actual pressure altitude shows that the apogee altitude of the simulation (2243 meter) matches within a small margin with the measured altitude of (2302 meters). However it must be mentioned that the time to apogee in the simulation (19.3 sec) mismatches the time to apogee of the measurement (22.2 sec). This could be assigned to several reasons:
• Inaccurate thrust and burn time data • Aerodynamic inertia in the flight computer compartment of the rocket. • Inaccurate aerodynamic model.
However, assuming the total impulse of the motors during the static firing tests and the flight are the same, and the altitude measurements of the rocket are accurate, the altitude prediction of the simulation is accurate within 3% as can be seen in Figure 4.22.
This validation shows that the predicted apogee altitude is within a 3% accuracy. Unfortunately there are not more datasets available on two stage rocket flights, thereby limiting the validation opportunity. One recommendation is to further investigate the validity of the simulation by comparing it with more rocket flights.
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.13 Flight parameter optimization
The drift time of the vehicle is defined as the time interval between the booster stage jettison and the ignition of the second stage.
Advantages of a long drift time: 87
• The longer the duration of this drift time, the higher the altitude where the second stage of the vehicle will be ignited. The aerodynamic drag loss of the second stage
lowers because of the decreasing density with altitude. imulation S -
• The ambient pressure is lower, enabling a higher performance of the second stage motor.
Chapter 4 Chapter • The altitude when igniting the second stage is higher.
Disadvantages of a long drift time:
• Energy is bled during the drift time, creating a lower second stage burnout velocity.
• The vehicle starts to arc, thereby pointing the new velocity vector less to the zenith, reducing the apogee altitude.
The simulation takes into account the arcing of the vehicle and the air-density, so the drift time can be optimized via a simple trail and error method in the simulation. The simulation can be run for instance for 100 times, with a variation of the drift time of 1 to 10 sec and an interval of 0.1 sec.
An example of a drift time optimisation can be seen in Figure 4.23. The optimum drift time is 5.2 sec, where the vehicle will reach a simulated apogee altitude of 14919 meter.
Figure 4.23: the iterative drift time optimization of the Stratos rocket.
. M.Sc. Thesis Mark Uitendaal B.Sc.
4.3.14 Failure scenario simulation
The simulation program is also used to simulate the flight trajectory in case of a failure. Since 88 there are numerous scenarios which the rocket could fail, some specific cases are identified:
Chapter-Simulation 4 • One booster motor ignition failure, up-wind and down-wind failure scenario. • Two booster motors failure, up-wind and down-wind failure scenario. • Thrust mismatch of the booster motors • Second stage ignition failure
If one booster motor ignition fails, it depends extremely on the wind condition what the vehicle is going to do. The thrust misalignment of the booster stage creates a moment, which can enhance or counteract the moment created by the aerodynamic forces due to side-wind.
The tower exit velocity will be lower because the total initial thrust of the rocket is only 75% of the nominal initial thrust, enhancing the effect of side wind [2].
Figure 4.24: the thrust-moment enhancing or counteracting the rotation caused by weather cocking.
Mark Uitendaal B.Sc. M.Sc. Thesis
89
imulation S -
Chapter 4 Chapter
Figure 4.25: a flight trajectory with one booster motor out, with a counteracting thrust moment.
Figure 4.26: a flight trajectory with one booster motor out, with a enhancing thrust moment.
. M.Sc. Thesis Mark Uitendaal B.Sc.
If two booster motors fail , the thrust is even 50% of the nominal situation. This situation is an more extreme version of the one booster motor failure scenario.
If the second stage of the vehicle ignition fails the flight trajectory will be very “interesting”. The vehicle will travel downwards with about 13.1 kilos of propellant, thereby creating a hazardous 90 situation. The impact point for this scenario is calculated for safety reasons.
Chapter-Simulation 4
Figure 4.27: a simulated flight trajectory of the Stratos when the second stage motor fails.
From Figure 4.27 it can be seen clearly seen that the Esrange requirement to launch at 80° elevation angle is a safety precaution. The fully loaded second stage will impact only 310 meters from the launch platform.
Mark Uitendaal B.Sc. M.Sc. Thesis
4.3.15 Operational parameter simulation
Another parameter which can be optimized is the launcher angle. The rocket will rotate against the wind due to its static stability. Because of this weather cocking effect, it can be advantageous to have a slight elevation angle with the wind. The rocket will rotate to a more 91 or less vertical trajectory after leaving the launch rail. This can also be optimized by a iterative simulation by varying angles and uniform wind conditions. However, Esrange limits the elevation angle to from 65° to 85°. The wind limitations are from 0 m/s to 7 m/s. imulation S -
Chapter 4 Chapter
Figure 4.28: the apogee altitude with iteration with uniform wind conditions and elevation angle
Another interesting point is the ballistic impact point. This determines the range which the rocket covers when the parachute is not deployed. This point varies with elevation angle and wind condition.
Figure 4.29: the ballistic range with iteration with uniform wind conditions and elevation angle.
These charts contain the operational parameters of the vehicle. These charts are extremely useful at the launch day, when a go/no-go for the launch is needed, to aid in with a limited
. M.Sc. Thesis Mark Uitendaal B.Sc.
amount of decision-time. The final launch elevation angle was set to 80° from the horizontal plane.
92 Chapter-Simulation 4
Mark Uitendaal B.Sc. M.Sc. Thesis
The Stratos rocket was produced in the facilities of the Delft University of Technology (DUT). The rocket was produced by volunteers of DARE. The production of a rocket vehicle is a good example of an interdisciplinary 93 production. 5.1 Production
production P
The production of the Stratos rocket can be split up into four production fields, apart from -
general fields like assembly: 5
• Composite • Propellant Chapter • Electronics • Metal parts
The composite production of the Stratos vehicle consists of the production of the nosecone, the motor casings, the fins, clamp band and the interstage fairing.
Composite materials are basically materials which consist of two material types: a reinforcement material, which provides the strength of the material and a matrix, which bonds the reinforcement material together. The matrix used for Stratos the Epicote 04908 resin. This resin, together with the Epicure 04908 was chosen because of its availability within the composite laboratories of the aerospace engineering faculty of the DUT. A overview of the Epicote system can be found in appendix E – The Epicote system. The reinforcement material chosen in the composite material depends on its application. For Stratos, two types of reinforcement materials were chosen: glass fiber, bidirectional woven, 200 gr/m 2 and carbon fiber, bidirectional woven.
For fins, a pre-produced material was used. A 3 mm thick quasi-isotropic bidirectional (0°/90°, 45°/-45°) carbon plate was used. Two plates of 3 mm where bonded together with an aerospace grade adhesive (3M 9323 B/A) to produce a 6 mm CFRP plate.
The composite production was mostly done at the composite laboratories of the aerospace engineering faculty of the DUT because of environmental and health concerns.
Propellant production consists of the preparation of the casting molds, the casting procedure itself, trimming and coating of the propellant grains. The mold preparation consists of mold manufacturing, coring rod lubrication and inhibitor preparation. Due to the lack of facilities by DARE, the actual casting and trimming of the propellant was done at the Dutch Amateur Rocket Research Association (NAVRO) in Alblasserdam. This implies a big logistical operation, transferring personnel, chemicals, tools and molds from Delft to Alblasserdam and back for several times.
The electronics production for the Stratos vehicle was done at the faculty of Electrotechnical Engineering (EWI building). The electronics were completely designed by DARE and build on CANSAT experience. Electronics can be split up into two parts: the hardware and the
. M.Sc. Thesis Mark Uitendaal B.Sc.
software. The software development is the programming of the firmware and overall software of the system. The software can be produced on several locations, and any updates can be connected to the DARE server via subversion (SVN).
The hardware is the Printed Circuit Boards (PCB’s) of the electronics, on which the components needs to be soldered. The soldering of the PCB’s was done at EWI on pre- 94 ordered PCB’s and components. First some test PCB’s were made on so called breadboards.
Chapter- 5 Production These test PCB’s were used to evaluate the first versions of the software. The lessons learned by constructing this PCB’s were used in the final design of the flight PCB’s.
Metal parts production was done in the PMB facility of the Design Engineering faculty of the DUT. Not all parts were produced in Delft. Some big, difficult or dull parts, such as the interstage coupler or the booster nozzles were produced in Belgium by the same company were DARE orders metal parts for CANSAT.
The parts produced at the PMB are the structure of the capsule section, the nozzle and endcap of the second stage motor, the pyrogen igniter and the final production of the interstage coupler.
After the production of the Stratos parts, these parts need to be assembled. Some parts are in a serial assembly process and some can be done in parallel .
A serial process is an assembly process where during the process the first part is needed to produce the second (or more) part(s). This is of course a problem, because some parts can only be made after another part is finished.
Figure 5.1: an example of a serial assembly process
A good example for serial production is the production of the booster clamp band. In order to make this part several other parts need to be completely produced:
• the marriage jig • the booster motor casings • the booster motor end caps • the booster motor nozzles • the interstage coupler
These parts need some time and some human recourse to be produced. Therefore, the booster clamp band can only be produced in a very late stage of the project. This implies for instance that the time between production and shipment for this part was very short. Problems that could arise during the production of such part need to be solved very quickly, or the delay will affect the shipment of the total vehicle and even the launch.
Mark Uitendaal B.Sc. M.Sc. Thesi s
The design of these later parts is simpler and special attention is given for easier manufacturing in order to outrun problems in the critical stage of the project.
In parallel assembly process, the manufacturing of the first part does not need to wait for the second part. This implies that the planning in production is much easier, since delay in one branch does not affect the total assembly of the vehicle. Some problems or delays in a part were expected and the production was planned accordingly. 95
production P -
5 Chapter
Figure 5.2: an example of a parallel assembly process
During the design of the Stratos it was recognized that the electronics of the vehicle will take up a lot of valuable time, since the expertise in that field of DARE was at that time not very high. The electronics were designed by a specialized team of more than 10 members dedicated to electronics. This team consists of 8 aerospace engineering students and 2 electro technical students. The aerospace engineering students were expected to have a learning curve, but this would take up much valuable time in the project.
The electronics were produced and planned totally separate from the rest of the vehicle. In order to accommodate this engineering approach, the capsule section was split and the flight computer section was able to perform stand alone operation.
During production a concept “Proto-flight” was explored, but with a backup capsule planned right after the first capsule. This was done to for several reasons:
• To have an active spare-part on standby during the launch campaign. • To make use of the learning curve of the production personal for the second part. • To allow testing on one capsule while the other capsule is still in production
In order to keep track of the part the capsule sections, names where given to the parts. The first section was called ANNABEL and was the Proto-flight version. On the second capsule section, which was called BETTY, most of the tests where performed.
The actual flight of the Stratos was made with capsule ANNABEL, where BETTY was on active standby during launch. If any problems would occur with ANNABEL, the BETTY capsule was ready to take its place.
. M.Sc. Thesis Mark Uitendaal B.Sc.
5.2 Production planning
The planning of production in projects with volunteers is different than ordinary production planning. Volunteers have concentrated moments where they are available, but this is not in a 96 linear time scale. It can be seen that close to a launch date the production rate and motivation of a voluntary group is very high. At other moment, for instance near an interim examination Chapter- 5 Production period, the student volunteers are not available for at least a month.
This was recognized during the project and a new production planning concept was created, named “Burst Production”. This concept is tries to optimize the production at the moments where production capacity is available. The “downtime” of voluntary capacity is used for production planning, simulations, re-designs of non-produced parts or making production drawings.
The burst production concept needs a new diagram, which shows the relation between each part and especially the serial relationships in the assembly process. The parallel relations in the planning are not displayed in the burst production diagram. An example of such a burst production diagram can be found in Figure 5.3.
The diagram is split up into sessions. In this diagram there are six sessions in four physical positions:
• PMB I • PMB II • COMPOSITE LAB I • COMPOSITE LAB II • DSA WORKSHOP • DARE WORKSHOP
The PMB and COMPOSITE LAB sessions are split up, because of some serial relationships between several parts in the production or the workload of the entire package was to much for the persons participating. Also some parts are split to introduce a learning curve. Such as for instance the parts for capsule ANNABEL where produced first. The lessons learned form the problem encountered during the production during these sessions could be implemented in the second session for the parts of capsule BETTY.
The final assembly was done in the DARE WORKSHOP session. This session was continuous and the availability of the workshop was not limited to normal office hours. The workshop was also used as a station area to store all completed parts which were ready for assembly.
Some parts cannot be produced in the DARE workshop, because of safety concerns. Such item contains for instance pyrotechnical components or propellant. The final assembly of the motors was done at the motor assembly bunker at Esrange. In order to explore the total amount of time necessary for producing a motor, a component flowchart was created per unit. An example can be found in Figure 5.4.
Mark Uitendaal B.Sc. M.Sc. Thesi s
97
production P -
5 Chapter
Figure 5.3: the production planning using the burst production concept.
Figure 5.4: a booster motor assembly flow chart
. M.Sc. Thesis Mark Uitendaal B.Sc.
98 Chapter- 5 Production
Mark Uitendaal B.Sc. M.Sc. Thesi s
In order to verify the simulation data, the empirical data of the motor tests and the flight were compared with the simulated results. 99
There are two types of simulated performance data:
• Motor performance simulations • Flight performance simulations
The motor performance simulations can be validated via static tests. In a static test the motor thrust is measured via a mechanical load cell. Other interesting data is the casing pressure, but
unfortunately this data is not available due to the lack of sensors. dataand flight analysis –
The flight performance simulations can only be validated with the flight data gathered with the flight of the Stratos rocket. The Stratos rocket contains sensors for gathering acceleration, GPS position and air pressure. This data is stored internally in the rocket on a non-volatile Chapter6 memory. Some data can be gathered externally during flight due to telemetry.
The flight simulation is programmed in such way that the program can generate outputs which are simulated results of the flight data.
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.1 The static tests of the rocket motors
On 23 October 2008, DARE did several motor tests on ASK ‘t Harde. The Opportunity rose because of the NLD28 launch of NAVRO, on which some launch-windows 100 were available for motor testing.
Chapter 6 –analysisflight and data The motors which were tested were: • Booster motor B3, in this report referred to as testmotor A • Booster motor B4, referred to as testmotor B • Second stage motor S3.
The reason for these tests was to provide motor test data which validated the motor simulation program and to provide motor performance data for the real launch. Esrange needs to have accurate motor performance data in order to simulate and assess the level of safety of the launch.
All the tests where performed in nozzle down position, so the thrust vector of the motor was directed vertically up. The load carrying structure used was “the gallow”, a structure of similar appearance, made out of 100 X 100 steel I beam and was specially designed for these and future static motor tests. The test construction can be seen in
The whole structure was about 4.5 meters tall, and dug 1.5 meters into the ground to attach it firmly to earth. In order to reduce vibrations the load carrying structure was also attached to the ground with two tethers and pins under pretension.
The motors were attached to the recording apparatus via two connection rings. These rings are padded with Delrin gliders in order to minimize friction and transfer the entire load to the recording apparatus. The rings can be attached to the load carrying structure at several positions to accommodate different motor lengths. The rings themselves can accommodate motor diameters of 140 mm.
Figure 6.1: “the gallow”, the load carrying structure used for the static tests.
Mark Uitendaal B.Sc. M.Sc. Thesis
The only parameter recorded during the tests was the motor axial thrust. This was done via a load-cell which was property of the faculty of Aerospace Engineering. The load cell could was ring shaped and could be loaded up to 10 KN. The load cell can be seen in Figure 6.2.
The tests were recorded at a sample-rate of 100 Hz. The data logger which was used was the DATAQ instruments DI-710-ULS, which could amplify the signal, digitize it via a 14 bit AD converter and store it to an SD-card. This data logger was constructed into a stand-alone unit 101 together with its power supply, a lead acid battery. The current configuration can have a operating time of over 17 hours of data collection and many hours more in standby modus.
The data logger, together with the power supply were inserted into a special box and dug into the ground in order to protect it from the exhaust-products.
flight dataand flight analysis –
Chapter6
Figure 6.2: the load cell, attached to the booster motor interface
Figure 6.3: the box with the data logger, protected by sand
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.1.1 The booster motors
The booster motors were tested on 3 different criteria:
• Performance of the booster motors 102 • Similarity in performance between the booster motors •
Chapter 6 –analysisflight and data Similarity in performance between the simulation and the booster motors
Two sample motors were constructed, which were the third and fourth motors produced in the total series. The two booster motors were data is summarized in Table 6.1:
Table 6.1: An overview of the two tested motors Motor A (test B3): Motor B (test B4): Propellant mass: 4.170 kg Propellant mass: 4.171 kg Total mass = 6.395 kg Total mass: 6.440 kg Burnout mass = 2.088 kg. Burnout mass 2.122 kg
The propellant grains of both motors were matched in such way that the total mass of propellant was as equal as possible. Also, since the propellant batches were casted in two separate sessions, the amount of grains in the motor from production-run A & B were the same in each motor (50/50), in order to reduce the possible difference between motor A and motor B.
A complete propellant mass data overview is given in Table 6.2. The masses provided in the table are exclusive inhibitor tube, made out of cardboard.
Table 6.2: the total propellant mass in the tested booster motors Grain Motor A Motor B number [gr] [gr] Remarks 1 526 524 2 524 524 3 522 522 4 536 538 5 510 520 coated 6 530 532 coated 7 528 526 coated 8 512 516 coated 9 176 162 starter grain Total mass 4364 4365 inc. inhibitors
The booster-motors were ignited via standard DARE igniters. These igniters consists of 1.5 grams of blackpowder (FFFF, supplier Vectran) and a Davey Bickford 1028 A00. The igniters were loaded though the nozzle and secured into place with on layer of ducttape (supplier Pattex)
Mark Uitendaal B.Sc. M.Sc. Thesis
6.1.1.1 Results of the booster motor tests
The booster motors performed similar results in startup behavior, thrust levels and burntime. Based on this result it can be confidently concluded that these motors are fit for clustering in the booster section of the Stratos rocket. 103 Some performance data of the two booster motors are given in Table 6.3.
Table 6.3: performance data from the booster motor test B3 and B4 Motor A B Remarks Total impulse [Ns] 4470 4542 Specific impulse [s] 109 110 Maxmimal thrust [N] 1542 1735 Some thrust oscillations
Burntime [s] 3.5 3.5 Between 10% F max (avarage) Avarage thrust [N] 1279 1297 flight dataand flight analysis – Initial mass [kg] 6.395 6.440 Burnout mass [kg] 2.088 2.122
Overall conclusion is that the booster motor design is fit for flight in quad-motor booster configuration, since no significant differences are seen in the performance of two nearly Chapter6 identical motors.
The thrust data gathered by the two tests are shown in Figure 6.4
. M.Sc. Thesis Mark Uitendaal B.Sc.
104 Chapter 6 –analysisflight and data
Figure 6.4: the thrust recordings of booster test B3 and B4
The thrust data from test B3 and B4 can also be compared with the thrust simulations of this is showed in Figure 6.5.
Mark Uitendaal B.Sc. M.Sc. Thesis
105
flight dataand flight analysis –
Chapter6
Figure 6.5: Thrust simulation compared with the actual thrust measurements of B3 & B4
The thrust diagrams of both motors are starting at t = 0 with ignition, in order to simulate the clustered situation as closely as possible, igniting the motors all simultaneously.
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.1.1.2 Comparison of the booster motor results with MPPT results
In comparison with the numerical simulation, the booster motors performed quite the same. However, the simulation is different on two points:
106 • The start-up period of the simulation differs with the results. The motor needs some Chapter 6 –analysisflight and data start up time of about 1.1 sec.
• The tail-off of the motor is not as simulated.
The start up behavior is different than expected based on the simulation. This is because the amount of black powder is too low to pressurize the motor to kick-start it right away. If the motor is pressurized till Maximum Expected Operating Pressure (MEOP), and the entire exposed burning surface is it according to the simulation, the motor can be started jut as the simulation
During the design, one of the biggest drivers, next to safety is the reliability of the motor. The composite casing was deliberately gradually stressed to it operating stresses, instead of an explosive start-up. It is believed by the author that the gradual pressure up of a rocket motor casing will reduce the risk of crack forming in stress concentrations regions.
The motors will ignite due to the heat transfer between the black powder charge and the grain surface. The energy conversion in the form of heat takes time. The motor will not produce adequate thrust until the gas velocity in the nozzle throat is supersonic. This will only happen if the mass flow in the nozzle reaches critical mass flow defined by Equation 4.17.
Reaching critical mass flow will take some time, because the first flux of hot gas, produced by the top grains will need to travel to the nozzle. The hot gas particles will lose energy because they will transfer energy to the cold exposed surface of the non-ignited grains. This exposed surface area will be ignited due to this extra energy, creating an extra flux of hot gas particles and fewer cold exposed grain-surfaces.
Due to this exponential process of ignition, it will take about 1.2 seconds for gas flow in the nozzle throat to reach critical mass flow. This depends of course on the amount of initiation charge, the amount of cold exposed surface area and the distance between the end cap and the nozzle.
The tail-off of the motor displays a different behavior than the simulation. Due to the non- linear behavior of the regression-rate over all the grains won’t be the same. The grains which suffer the most from erosive burning are the grains with the highest gas velocity in the core. Those grains are located the most close to the nozzle. These grains will be spent faster than the grains which are located near the end cap.
Due to this phenomenon, the burning surface area of the grains is lower than anticipated in the end phase of the motor burn; therefore, the thrust will be lower.
Mark Uitendaal B.Sc. M.Sc. Thesis
6.1.2 The second stage motor
On the same test-campaign, the second stage motor of the Stratos rocket was tested. This test was refered to as test S3. The motor pre-firing data (test S3) was:
Propellant mass (including web-thickness smoke grain): 12.31 kg. 107 Total mass: 20.1 kg (including forward and rear skirts) Burnout mass: 6.464 kg (including forward and rear skirts)
The exact propellant distribution per grain-segment can be found in Table 6.4.
Table 6.4: the mass of the propellant grains of the second stage motor Grain number Grain mass [gr] Remarks
1 1806
flight dataand flight analysis
2 1824 –
3 1748 4 1822 5 1740 coated 6 1820 coated Chapter6 7 1762 coated 8 1454 starter/smoke grain
Total mass 13976 inc. inhibitor and smoke grain
The ignition for this motor is done with the pyrogen igniter which is elaborated in section 2.6. The squibs used for this test are two redundant Davey Bickford 1028 A00 squibs. These squibs are geometrical similar as the squibs used at the launch site, although the costs per squib is reduced by a factor two.
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.1.2.1 Results of the second stage motor tests
The second stage motor was tested on two criteria:
• 108 Performance of the second stage motor • Similarity in performance between the simulation and the second stage motor. Chapter 6 –analysisflight and data The motor is also designed to produce smoke after the thrust duration in order to reduce aerodynamic drag during the coasting phase of the flight. Since the mass flow in the nozzle doesn’t reach critical mass flow, the thrust generated by only the smoke grain is negligible.
A conclusion of the performance is presented in Table 6.5
Table 6.5: performance data from second stage motor test S3
Motor S3 Remarks Total impulse [Ns] 15600 linear massflow assumption Specific impulse [s] 129 calculated over propellant Maxmimal thrust [N] 4305 spike Thrust oscillations
Burntime [s] 4.8 between 10% F max Avarage thrust [N] 3250 Initial mass [kg] 20.1 including skirts Burnout mass [kg] 6.464 including skirts
Mark Uitendaal B.Sc. M.Sc. Thesis
The thrust measurement of the second stage motor test S3 is presented in Figure 6.6.
109
flight dataand flight analysis –
Chapter6
Figure 6.6: The measurements from test S3
. M.Sc. Thesis Mark Uitendaal B.Sc.
These thrust measurements, compared with the simulations are presented in
110 Chapter 6 –analysisflight and data
Figure 6.7: the simulations compared with the measurements.
Mark Uitendaal B.Sc. M.Sc. Thesis
6.1.2.2 Comparison of the second stage motor results with MPPT
The simulation and the measurements are different in several points:
• After 2 sec after thrust-up the thrust and the simulation begin to differ dramatically 111
• The burn time of the motor is a little shorter than expected in the simulation
• The overall specific impulse (I sp ) of the motor is slightly higher than expected (2.3%).
• Some oscillations in the thrust measurements are showing in the powering down phase (t = 4 sec).
After 2 seconds the thrust-profile shape differs dramatically from the shape of the simulation. It flight dataand flight analysis
appears an extra “bulge” in the thrust profile is forming after 2 seconds in the burn. It seems – some other physical phenomenon is present in the motor, which is not incorporated in the simulation. Because of the delayed action it is probable that this has something to do with thermodynamics in the combustion process, which results in a higher regression rate than simulated. Further investigation into this phenomenon is required in order to complete the Chapter6 simulation. This implies new and expensive static tests with big scale motors to model this behaviour.
The burn time is a little longer than expected in the simulation. This related to the higher regression rate observed by the fact that extra thrust is generated by an unknown phenomenon.
Thrust oscillations are noticed at about 4 seconds after thrust up. This is in the powering down phase of the motor burn. Further investigation is needed if this is in the motor test set-up due to stress relaxation or in the actual motor performance.
The ignition delay of the second stage motor, which is also very important for the optimization of the drift-time, is slightly longer than expected. This can be explained due to the longer motor length and the higher amount of cold exposed grain surface area.
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.2 Results of FTPS: the nominal flight trajectory
For the flight of the Stratos rocket, some initial simulation where run in order to simulate important flight parameters. In order to attain relevant data, a “nominal flight trajectory” was 112 established. This nominal launch condition where defined as:
Chapter 6 –analysisflight and data • Atmospheric temperature and pressure distribution as in Esrange sample measurement
• Wind situation: 0° at uniform 4 m/s.
• Tower elevation: 80° from horizontal
• Tower azimuth: 0°
• Booster motor performance: 2 booster motors B3 thrust profile 2 booster motors B4 thrust profile
• Second stage motor performance: S3 thrust profile
• Drift time between booster separation and ignition signal: 4.8 sec
Because the actual vehicle was not built at this point in the project, the flight simulation had to be performed with vehicle data which was a mass estimation of the vehicle. For the Stratos nominal flight trajectory this was:
• Capsule mass: 3 kg
• Fins of the second stage: 1 kg
• Interstage coupler + booster fins: 3.5 kg.
The aerodynamic parameters of the rocket models can be found in appendix B – the aerodynamic parameters.
Mark Uitendaal B.Sc. M.Sc. Thesis
With the nominal launch conditions, the output of the simulation is summarized in Table 6.6
Table 6.6: simulation summary Tower exit velocity [m/s] 36.46 Altitude booster burnout [m] 953 Mach number booster burnout 0.93 Altitude second stage ignition [m] 2168 113
Mach number second stage ignition 0.7 Altitude second stage burnout [m] 5622 Mach number second stage burnout 2.67 Apogee altitude [m] 14996 Impact range [m] 14321
An altitude-range plot of the nominal flight trajectory can be found in Figure 6.8. flight dataand flight analysis –
Chapter6
Figure 6.8: the nominal flight trajectory of the Stratos rocket
This nominal flight conditions shows that the apogee altitude is located about 40% higher than the European altitude record for amateur rockets claimed by the MARS team. This result validates the record attempt. Other important plots from this nominal flight trajectory can be found in appendix C- Performance plots of the nominal flight trajectory.
This nominal flight condition is the cases which were presented to Esrange. This flight trajectory was evaluated by Esrange and the Swedish authorities in order to permit the flight of the Stratos at the Esrange Space Centre.
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.3 The launch
On the 17 th of March 2009 at 10.28 UTC, the Stratos rocket was launched at the Esrange Space centre, about 40 km east of Kiruna, Sweden. The Rocket was launched from the 114 specially prepared DARE launch tower, positioned on the MAXUS launch platform in the west part of the launch complex. Details of the launch position can be found in Table 6.7. Chapter 6 –analysisflight and data Table 6.7: some properties of the launch position Tower lenght [m] 6 Tower azimuth [deg] 355 Tower elevation [deg] 80 Launcher position (lat [dddd], long [dddd], alt [m]) 67.8933, 21.1040216666667, 336.6 Temperature [°C] ± -5 Wind (estimation) [m/s, deg] 5 m/s, 300
The Stratos rocket reached an apogee altitude of 12215 m above the launchpad, about 2800 m short of its expected altitude. The parachute didn’t open as expected and the capsule section impacted about 16 km from the launch site in a remote and unreachable area.
The wreckage of the rocket is up till the publication of this report not found. This implies that the internal data storage can’t be accessed. This implies that the acceleration and pressure sensor data isn’t available for evaluation.
In the Stratos there was also a telemetry unit available. Telemetry is the technology to perform measurements with a sensor and send those measurements via radio technology to a receiving station for evaluation.
The only data which is available from telemetry are:
• State changes from the flight computers
• GPS data from the ETAG system
• Doppler shift in the telemetry data
Mark Uitendaal B.Sc. M.Sc. Thesis
6.3.1 State changes
The actual data which is broadcasted was for the telemetry system the changes in the state of the software via an audio beeping code. The operators of the rocket vehicle record the audio which is broadcasted by the vehicle for later flight evaluation. 115 Since the requirements for the state changes are known, certain data points in the flight profile can be reconstructed. A list of the received state changes can be seen in Table 6.8.
Table 6.8: the state changes as received by the DARE telemetry station
Event Time from lift-off [m:s] Lift-off 0:00:01 Burnout 0:00:05 Go 0:00:10 flight dataand flight analysis –
No-Go 0:00:15 Apogee 0:00:27 Apogee altitude BC 0:00:49 No-Go Drogue 0:01:13 No-Go Parachute 0:01:38 Chapter6 Loss Of Signal (LOS) 0:01:56
It can be seen clearly from Table 6.8 that at 10 seconds after lift-off, the flight computer switches to a “Go” state. In this “Go” state, the second stage motor was ignited.
However, during the 5 seconds after this event, the system couldn’t detect the acceleration and automatically switched to the “No-Go” state. The timing values for drogue where reset to appropriate values for a “No-Go” scenario. This implies a forced drogue deployment 60 seconds after initiation of the “No-Go” scenario.
Figure 6.9: the followed track through the software states during the flight
However, 1 second after initiation of the “No-Go” state a Doppler shift was noticed by the operators of the telemetry station, indicating a thrust-up of the second stage motor.
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.3.1.1 Conclusions from the state changes
From the state changes it can be concluded that the flight computer switched to the “No-Go” state while the second stage motor of the rocket was still thrusting up to full thrust.
116 The actual thrust-up of the second stage motor happened 1 second after the window for Chapter 6 –analysisflight and data ignition detection was closed. The thrust-up behaviour of the second stage motor at the flight conditions was not the same as in the static test S3 performed at sealevel conditions.
The drogue parachute was forced to initiate at 60 seconds after the “No-Go” decision. The altitude at the moment of first and second pyrocharge initiation was according to the ETAG data about 11 km. The static pressure at that altitude is approximately 20 KPa.
Mark Uitendaal B.Sc. M.Sc. Thesis
6.3.2 ETAG
The “Esrange Throw Away GPS” or abbreviated ETAG, is originally a balloon tracking system developed by the Swedish Space Cooperation. The internal GPS in the ETAG unit calculates its position with a rate of 1 Hz. This position is broadcasted via Very High Frequency (VHF) radio (173.225 MHz. which is referred to as the Esrange E-link system). 117 The ETAG unit is a PCB of 100 X 40 mm which is located in the tip in the nosecone protected by a conical shaped foam fairing.
flight dataand flight analysis –
Chapter6
Figure 6.10: The ETAG unit, provided by SSC (picture SSC)
Figure 6.11: the ETAG in its foam protection for the Stratos rocket
. M.Sc. Thesis Mark Uitendaal B.Sc.
The ETAG was used to track the flight of the Stratos rocket. The flight path of the rocket could be tracked with a refresh rate of 1 Hz. In order to ensure a proper measurement of position, the GPS is switched on without an operating telemetry system. This procedure is called a “hotfix” so the GPS unit has about twenty minutes to calculate its position.
118 However, if the GPS loses its fix, the last known position is broadcasted via the telemetry
Chapter 6 –analysisflight and data system.
The precise data points of the ETAG can be seen in appendix F – ETAG data. The points where plotted in a three-dimensional coordinate system, as can be seen in Figure 6.12.
Figure 6.12: the flight trajectory in three-dimensional coordinates of the Stratos rocket as received from the ETAG
Since the flight simulation program is a two-dimensional simulation, the three-dimensional data is reduced to a two-dimensional dataset. This done via a transformation as can be seen in Equation 6.1.
Mark Uitendaal B.Sc. M.Sc. Thesis
R = X 2 + Y 2 Equation 6.1
Where R is the range of the rocket and X and Y are the ground coordinates of the rocket in meters, defining the launch platform as its origin. 119
The flight simulation program can be matched to the founded results with the following altered parameters:
• Single stage model has a 5% higher Cd value
• The two stage model has a 3% higher Cd value
• The time between separation and motor thrust-up is 9.5 seconds flight dataand flight analysis
–
• There is no drag reduction due to the presence of the smoke grain.
The results obtained with this simulation can plotted over the flight data as can be seen in
Figure 6.13. Chapter6
Figure 6.13: the flight trajectory in two-dimensional coordinates of the Stratos rocket as received from the ETAG
. M.Sc. Thesis Mark Uitendaal B.Sc.
6.3.3 Doppler shift
Doppler shift is the change in frequency, due to a velocity by the oscillating source, or the 120 observer. The effect was discovered by the Austrian physicist Christian Doppler, in 1842. The effect can be described via Equation 6.2. Chapter 6 –analysisflight and data
v − c f = f 0 v + c Equation 6.2
Where:
v = the speed of the moving object, emitting the electro magnetic radiation [m/s] c = the speed of light in vacuum which is 299,792,458 m/s
With this phenomenon it is possible to calculate the relative velocity between the source and the receiver by measuring the frequency shift of the received radio signals.
In case of the telemetry, the telemetry receiving station is on a fixed position about 1200 meters orthogonal on its flight path. The relative velocity, which the source is traveling away, is not the same as the airspeed of the vehicle. This relative velocity is also referred to as “slant- velocity”.
This velocity can be calculated by rewriting Equation 6.2 to Equation 6.3.
f 2 1− w f 0 v = c ⋅ f 2 −1⋅ w +1 f 0 Equation 6.3
Mark Uitendaal B.Sc. M.Sc. Thesis
The frequency shift over time of the telemetry can be observed if the received audio is plotted via a so called “waterfall-diagram”.
121
flight dataand flight analysis –
Chapter6
Figure 6.14: the waterfall diagram, with all harmonic frequencies
Several points are interesting to know the exact slant-velocity of the vehicle on the following events:
• Booster burn-out • Second stage ignition • Second stage burnout
These events will show up as distinctive points in the frequency shift plot of the telemetry as can be seen in Figure 6.15 .
. M.Sc. Thesis Mark Uitendaal B.Sc.
122 Chapter 6 –analysisflight and data
Figure 6.15: the interesting velocities in the frequency shift profile of the telemetry
The exact values according to the waterfall diagram are:
• Stand still 4014 KHz. • Booster burn-out 3820 KHz. • Second stage ignition 3709 KHz. • Second stage burn-out 2855 KHz.
The audio frequency is added to the carrier frequency of 433.1608 MHz.
The exact slant velocity can now be calculated via Equation 6.3, resulting in a slant velocity of:
• Booster burn-out 211 m/s • Second stage ignition 135 m/s • Second stage burnout 802 m/s
Mark Uitendaal B.Sc. M.Sc. Thesis
The altered flight simulation can also simulate what a telemetry receiving station placed 1200 meters orthogonal on the flight trajectory plane should receive as relative velocity.
123
flight dataand flight analysis –
Chapter6
Figure 6.16: the Doppler measurement points in the simulation, measured in relative, or “slant- velocity”
According to this simulation the relative velocity on the 3 interesting points are:
Table 6.9: comparison of the relative velocity by Doppler measurements and the simulation Event Doppler measurement [m/s] Simulation [m/s] Error [%] Booster burn-out 211 222 5 Second stage ignition 135 155 13 Second stage burn-out 802 775 3
It can be seen clearly that the booster motors performed better than in the static tests, delivering a higher burnout velocity than expected. The simulated relative velocity at second stage ignition proves to be 13% higher than the measured result. This can be subscribed to a different aerodynamic model and different second stage motor performance.
. M.Sc. Thesis Mark Uitendaal B.Sc.
The second stage reached a 3% lower burn-out velocity. This can be subscribed to two possible reasons:
• The second stage motor underperformed, maybe because of the bad start-up characteristics, because of the lower static pressure.
124 • The supersonic drag properties of the single stage model of the simulation are Chapter 6 –analysisflight and data optimistic, but the sub-sonic drag properties of the single stage model are pessimistic
The total Doppler shift can be projected over the Slant velocity simulation. It can clearly be seen that both graphs are strikingly similar in shape.
Figure 6.17: an overlay of the simulated relative velocity and the Doppler shift on the received signal.
Mark Uitendaal B.Sc. M.Sc. Thesis
7.1 Conclusions 127
The booster motors in test B3 and B4 performed as expected via the motor performance simulation. The second stage motor shows an extra “bulge” in the thrust profile. It seems some other physical phenomenon is present in the motor, which is not incorporated in the simulation. Further investigation into this phenomenon is required in order to complete the simulation. Both motors where fit for flight in the Stratos rocket.
The Stratos rocket did meet its goal of breaking the European Altitude record for amateur rockets. The rocket reached a verified apogee altitude of 12215 meters above the launch platform, thereby breaking the European altitude record for amateur rockets Hereby, the first recommendations and project objective as stated in chapter 1 was fulfilled.
The difference in the simulation and the actual flight altitude is about 2800 meters. This
difference between the nominal scenario and the actual flight is caused by the longer thrust-up Conclusions – time of the second stage motor. When a simulation is performed with a altered thrust-up time, the difference in simulated burn-out velocity and actual relative burnout velocity is about 25 m/s, thereby concluding that the simulation is within 3% accurate.
Chapter7 The thrust-up time of the second stage motor at the ignition altitude was almost three times as long than at sea level. Most likely, this is caused by the low static pressure at that altitude, influencing the ignition system of the second stage motor.
Due to the thrust-up time of second stage motor, which was longer than anticipated, the flight computers switched to the back-up scenario. Due to this scenario, the EED of the drogue mortar was initiated at approximately 11 km, resulting in a failure of the recovery deployment system, since this is outside of the usage envelope of the system.
At 11 km, the static pressure of 20 KPa is according literature [2] to low to initiate a black powder charge, due to its high pressure exponent. Further investigation needs to be done on this subject in order to verify this conclusion.
The rocket crashed at Esrange with an impact velocity of 230 m/s. The rocket is not found up to this point of writing and the invaluable internal flight data is not available for analysis, however the telemetry system can be used to confirm the apogee altitude, impact point and burn-out velocity.
The knowledge of DARE was further expanded by this project and the visibility of DARE is further increased within the DUT and the space community, fulfilling the second an third project objective. The fact that this rocket is actually launched at Esrange implies that the also all the project objectives are fulfilled.
. M.Sc. Thesis Mark Uitendaal B.Sc.
7.2 Recommendations
Projects such as the Stratos project can be part of the curriculum of the master of Aerospace engineering. However, it is recommended that such projects have a higher degree of graduate 128 participants on critical positions in the project, since the amount of time available for a graduate is higher than for a volunteer. Chapter-Conclusions 7 andrecommendations The actual conditions which the DMA was initiated should be reproduced, where it can be verified if the low static pressure is the reason why this pyrotechnical device didn’t performed as intended. This device was however used outside its usage envelope.
DARE and/or DUT should invest in propellant casting, characterization and test-facilities in order to produce and test these amounts of propellant involved in this scale of projects. The possibility of using test facilities to simulate ignition behaviour of pyrotechnics at lower static pressures should be investigated.
The MPPT should be developed further to incorporate the difference in performance prediction of bigger solid rocket motors. A thermal model should be made and integrated within the MPPT.
Manufacturing problems, such as problems with using different mandrill shapes, or bigger composite casing should be investigated, in order to further expand the usage envelope of the solid propellant used today. Other investigations should be done to create a safe, reliable and affordable solid rocket propellant with higher performances than the propellant used with the Stratos project.
Mark Uitendaal B.Sc. M.Sc. Thesis
[1] Mulder, J.A. et all, Flight Dynamics, Lecture Notes AE3-302, February 2007, Delft 129 University of Technology
[2] Uitendaal, M., Amateur raketbouw projecten, 2006
[3] Fleeman, Eugene L., 2001, Tactical missile design, AIAA education Series, first edition Bibliography
[4] Ambrosius, B.A..C., Wittenberg, H., Rocket Motion & Re-Entry, Lecture Notes AE4-870, November 2006, Delft University of Technology
[5] Sutton G.P, rocket propulsion elements, 2001 Prentence Hall
[6] Wijker, J.J., Spacecraft Structures, Lecture Notes AE4-537, September 2006, Delft University of Technology
[7] Zandbergen, B.T.C., Thermal Rocket Propulsion, Lecture Notes AE4-S01, Version 2.03, Delft University of Technology
[8] G.J.J. Ruijgrok, Elements of airplane performance, third editions, Delft university press, 1996
[9] L. Meriam & L.G. Kraige, 1998, Engineering mechanics Dynamics, fourth edition, John Wiley & Sons, Inc
[10] Hamann, R.J., van Tooren, M.J.L., Systems engineering and technical management techniques, Lectrure Notes AE3S01, January 2004, Delft University of Technology
. M.Sc. Thesis Mark Uitendaal B.Sc.
A.1 The analytical results compared to the simulation 131
The simulated results can be compared to the analytical results. With the analytical method, the velocity of the vehicle is directly calculated. Altitude gains are derived form this velocity increments via integration. Errors due to inaccuracies and assumptions in the analytical velocity calculation are exaggerated via the integration method, influencing the validity of the comparison. Due to this phenomenon, only the analytically calculated velocity is compared with the simulated velocity .
For the simulation, the nominal flight trajectory is chosen. The velocity of the simulated results analytical The nominal flight trajectory can be seen in –
Appendix A A Appendix
Figure A.1: the simulated velocity of the nominal flight trajectory
Where 3 important points are examined with their simulated result:
• Booster burn-out velocity 325 m/s • Second stage ignition velocity 200 m/s • Second stage burn-out velocity 850 m/s
. M.Sc. Thesis Mark Uitendaal B.Sc.
The analytical results where used to verify the simulated results and check them on feasibility. In order to calculate the predicted burn-out velocity, the famous rocket formula of Tsiolkovskii can be used, which is also shown in chapter 1 – Rocket design as Equation A.1.
M ∆V = V ln 0 burnout e M 132 e Equation A.1
Appendix A – TheAppendixA analytical – results In which:
• Vburnout = burnout velocity [m/s] • M0 = initial mass [kg] • Me = burnout mass [kg] • Ve = effective exhaust velocity [m/s]
In order to do that, several parameter need to be calculated:
• The initial and total mass of the two stage model • The initial and total mass of the single stage model • The effective exhaust velocity of the booster motors • The effective exhaust velocity of the second stage motor
Of course the effective exhaust velocity of a rocket can also be expressed as Equation A.2.
V = I ⋅ g e sp 0 Equation A.2
Where:
• Ve = effective exhaust velocity [m/s] • Isp = specific impulse [s] • 2 g0 = gravitational acceleration, assumed 9.80665 m/s
The Isp of the booster motors is set as 109.5 sec. as can be seen in Table 6.3, which result in an effective exhaust of 1074 m/s.
The second stage motor has an I sp of 129 sec. as can be seen from Table 6.5. It must be mentioned that this I sp is measured at sea level, and the actual operating conditions of the second stage motor are in far lower conditions. The specific impulse of static test S3 will result in a effective exhaust velocity of 1265 m/s.
Table A.1: the data for the analytical calculation for the burnout velocity Two stage model Single stage model Total mass [kg] 54.9 26 Propellant mass [kg] 17.15 12.3 effective exhaust velocity [m/s] 1074 1265
Mark Uitendaal B.Sc. M.Sc. Thesis
A.2 The booster burn-out velocity
The booster burnout velocity can now be calculated via Equation A.1 as:
1074 ⋅ ln 54 9. = 402 37 75. m/s 133 Equation A.3
The booster experiences some gravitational loss and aerodynamic loss during the burntime.
The gravitational loss can be calculated via Equation A.4.
∆V = t ⋅ g gravitatio nal burn 0 Equation A.4 The analytical results results analytical The
– Where:
• tburn = the burntime of the motors [s] 2
• A Appendix g0 = the gravitational acceleration of 9.80665 m/s
Now the ∆Vgravitatio nal during the burn is set at 34 m/s.
The aerodynamic drag of the rocket can be calculated via Equation A.5
1 ⋅ ρ ⋅ V 2 +V 2 ⋅ c ⋅ A ( 0 e ) d ref ∆V = 4 ⋅ t aerodrag m burn Equation A.5
In which:
ρ = the air density [kg/m 3]
V0 = the velocity in the beginning of the burn (0) [m/s] Ve = the burnout velocity [m/s] cd = the aerodynamic drag coeffiecent , set at 0.75 [-] Aref = the reference surface of the two stage model
Now the aerodynamic drag loss during the burn can be set as 22 m/s
This gives a total loss of 56 m/s. The analytical burnout velocity of the booster should now be approximately 346 m/s. Of course a lot of assumptions are made here, such as:
• Constant aerodynamic drag coefficient c d calculated over a constant average velocity regime • vertical rocket flight • During the burn the mass of the rocket stays constant (average of the full and empty mass)
. M.Sc. Thesis Mark Uitendaal B.Sc.
The simulated booster burnout velocity is calculated as 325 m/s which is about 7% lower. Since the simulation takes much more variables into account, such as mach-effects and density differences, it can be concluded that the simulated results are valid. A.3 the velocity of second stage ignition
134 The velocity which the vehicle travels at the ignition of its second stage can be calculated by
Appendix A – TheAppendixA analytical – results summing up the booster burn-out velocity and the total losses during drifting.
The nominal drift-time of the vehicle is 4.8 seconds. The thrust-up time of the second stage motor is 2 seconds. The total drift-time should be 6.8 seconds.
In 6.8 seconds the rocket should decelerate about 67 m/s according to Equation A.4.
The drag losses during drifting can be calculated with Equation A.5, which will result in a drag loss of approximately 93 m/s.
This will result in a total velocity decrement of approximately 160 m/s.
The second stage ignition occurs analytically at approximately 186 m/s. This compares to the simulated result of 200 m/s with an error of about 7%.
A.4 the burnout velocity of the second stage
The burnout velocity of the second stage can be calculated according to Equation A.1 with the values of Table A.1 to:
1265 ⋅ ln 26 = 810 13 7. m/s
Equation A.6
The second stage experiences also some gravitational loss and aerodynamic loss during the burn time. The gravitational loss calculated via Equation A.4 and is set at 47 m/s
The aerodynamic drag loss can be calculated via Equation A.5, with an average air density of only 0.9 kg/m 3. This velocity loss during the burn is calculated as 225 m/s.
The total velocity decrement during the motor-burn is approximately 272 m/s. This will result in a motor burnout velocity of 738 m/s which is within 13% accuracy of the simulated results of 850 m/s.
Mark Uitendaal B.Sc. M.Sc. Thesis
B.1 The aerodynamic parameters as used in the simulations 135
In order to simulate the aerodynamic characteristics of the Stratos vehicle, some aerodynamic parameters must be used. These parameters, provided by the AEROLAB model are:
• Drag coefficient • Position of the centre of pressure • Lift slope coefficient
The drag coefficient can be divided into three cases:
• powered two stage model The aerodynamic parameters aerodynamic The
• –
unpowered single stage model • powered single stage model B
The unpowered two stage model is missing, because this situation does not occur, since the
booster is dropped immediately after burnout. Appendix
Figure B.1: the drag coefficient of the two stage model in powered flight
. M.Sc. Thesis Mark Uitendaal B.Sc.
136 AppendixBThe aerodynamic– parameters
Figure B.2: the drag coefficient of the single stage model in unpowered flight
FigureB.3: the drag coefficient of the single stage model in powered flight
Mark Uitendaal B.Sc. M.Sc. Thesis
The position of the centre of pressure is calculated from the tip of the nosecone and is given in mm. The total length of the rocket changes with the jettison of the booster section, therefore the magnitude of position of the centre of pressure varies.
137
The aerodynamic parameters aerodynamic The
–
B Appendix Appendix
Figure B.4: the position of the centre of pressure of the two stage model
Figure B.5: the position of the centre of pressure of the single stage model
. M.Sc. Thesis Mark Uitendaal B.Sc.
The Lift slope coefficient of the vehicle varies with the Mach number.
138 AppendixBThe aerodynamic– parameters
Figure B.6: the lift slope coefficient of the two stage model
Figure B.7: the lift slope coefficient of the single stage model
Mark Uitendaal B.Sc. M.Sc. Thesis
C.1 Performance plots of the nominal flight trajectory 139
The nominal flight trajectory of the Stratos rocket is elaborated in appendix C. The vehicle performance plots presented from this situation are: trajectory
t • Altitude vs. range • Altitude vs. time • Thrust vs. time • Mass vs. time • Acceleration vs. time • Velocity vs. time • Mach number vs. time • Angle of attack vs. time • Static margin vs. time
The environment where the simulation is set is explained in the following plots:
• Temperature vs. altitude ofnominal fligh the plots Performance –
• Pressure vs. altitude C • Wind vs. altitude
Appendix
. M.Sc. Thesis Mark Uitendaal B.Sc.
The vehicle performance plots of the nominal flight trajectory
140
AppendixC Performance the– plots nominal of fligh
t trajectoryt Figure C.1: the altitude range plot
Figure C.2: the altitude vs. time plot
Mark Uitendaal B.Sc. M.Sc. Thesis
141
trajectory t
Figure C.3: the thrust vs. time plot Performance plots of the ofnominal fligh the plots Performance – C C Appendix
Figure C.4: the vehicle mass vs. time plot
. M.Sc. Thesis Mark Uitendaal B.Sc.
142
AppendixC Performance the– plots nominal of fligh
Figure C.5: the acceleration vs. time plot
t trajectoryt
Figure C.6: the velocity vs. time plot
Mark Uitendaal B.Sc. M.Sc. Thesis
143
trajectory t
Figure C.7: the Mach number vs. time plot
Performance plots of the ofnominal fligh the plots Performance – C C Appendix
Figure C.8: the angle of attack vs. time plot
. M.Sc. Thesis Mark Uitendaal B.Sc.
144
AppendixC Performance the– plots nominal of fligh
Figure C.9: the static margin vs. time plot t trajectoryt
Mark Uitendaal B.Sc. M.Sc. Thesis
The environmental data of the nominal flight trajectory.
145
trajectory t
Figure C.10: the temperature vs. altitude plot Performance plots of the ofnominal fligh the plots Performance – C C Appendix
Figure C.11: the pressure vs. altitude plot
. M.Sc. Thesis Mark Uitendaal B.Sc.
146
AppendixC Performance the– plots nominal of fligh
Figure C.12: the wind speed vs. altitude plot. On request of Esrange, this was set to a uniformly distributed wind speed of 8 knots, or 4.12 m/s. t trajectoryt
Mark Uitendaal B.Sc. M.Sc. Thesis
D.1 The outline of the Stratos rocket 147
The outline of the Stratos Stratos rocket ofoutline the The – D D Appendix
Figure D.1: the dimensional overview of the Stratos rocket
. M.Sc. Thesis Mark Uitendaal B.Sc.
148
AppendixC Performance the– plots nominal of fligh t trajectoryt
Mark Uitendaal B.Sc. M.Sc. Thesis
The Epicote system 149
Features
• Certified by German Lloyd • Low viscosity • Extended pot life • Low exothermic heat
System Epicote The – Application
Low viscous resin system designed for infusion applications with excellent wetting and adhesion characteristics on fibreglass, carbon- or aramid-fibres, particularly in boats and yacht- building and production of rotor blades. This system makes it possible to manufacture APPENDIX APPENDIX E construction elements of a superior quality, with outstanding surface characteristics and good resistance to thermal deformation and weathering.
Processing Details:
Mixing ratio
• EPIKOTETM Resin 04908 100 parts by weight • EPIKURETM Curing Agent 04908 30 parts by weight
Mixing tolerance
The maximum allowable mixing tolerance is ± 2 pbw, but it is particularly important to observe the recommend mixing ratio as exactly as possible. Adding more or less hardener will not effect a faster or slower reaction - but an incomplete curing which cannot correct in any way. Resin and hardener must be mixed very thoroughly. Mix until no clouding is visible in the mixing container. Pay special attention to the walls and the bottom of the mixing container. Processing temperature
. M.Sc. Thesis Mark Uitendaal B.Sc.
A good processing temperature is in the range between 25 °C and 35 °C. Higher processing temperatures are possible but will shorten the pot life. A rise in temperature of 10 °C reduces the pot life by approx. 50 %. Different temperatures during processing have no significant effect on the strength of the hardened product.
150 Do not mix large quantities at elevated processing temperatures. The mixture will heat up fast
APPENDIXTheE Epicote– System because of the dissipating reaction heat (exothermic reaction). This can result in temperatures of more than 200 °C in the mixing container.
Exemplify curing cycle:
• 4 - 6 h at 80 °C
The values are measured on laminates made with glass fabric 181/Interglas 91745.
Mark Uitendaal B.Sc. M.Sc. Thesis
Shelf life
The resin and hardener can be stored at 20 - 25 °C for at least 12 months in their carefully sealed original containers. It is rarely possible that the resin or the hardener crystallize at temperatures below 15 °C. The crystallisation is visible as a clouding or solidification of the content of the container. Before processing, the crystallisation must be removed by warming up. Slow warming up to 50 - 60 °C in a water bath or oven and stirring or shaking will clarify 151 the contents in the container without any loss of quality. Use only completely clarify products. Before warming up, open containers slightly to permit equalization of pressure. Caution during warm up! Do not warm up over open flame!
Precautions
For information about safe handling of EPIKOTE epoxy resins and EPIKURE Curing
Agents, please note the corresponding Safety Data Sheet. System Epicote The –
APPENDIX E
In the process of international testing system harmonization, the national standards previously used are being increasingly replaced by ISO (DIN EN ISO) standards. All information, recommendations and suggestions offered by Hexion Specialty Chemicals GmbH, whether orally, in written form or in database, are provided to the best of our knowledge and belief. However, they may not be construed as legally binding statements and do not represent the basis of either a guarantee or specification. The same applies analogously o the data parameters stated for examples of cured binder systems; these represent analytical results and are only intended to simplify advance selection of the individual components of a binder. This information, these recommendations and suggestions describe our products and possible applications in general or exemplary terms, but do not refer to specific cases. Changes in the data parameters, texts and illustrations can result from the constant process of technical development and improvement of our products; possible changes are not specially mentioned in the text. Our support does not free the customer from the obligation to conduct this own review of our current information literature, in particular our product data sheets, safety data sheets and technical information leaflets. The customer must carry out tests of our products on its own responsibility to determine their suitability for the intended processes and uses, as well as to establish whether their processing characteristics are appropriate in a specific case, since the technical uses of our products are numerous and can vary widely in a specific instance. Therefore, such factors do not fail within our control, and are the exclusive responsibility of the customer. If a specific assurance of data parameters should be required, an appropriate agreement must be reached to this effect. Any applicable patents, existing laws and regulations must be observed by the customer or user of our products on its own responsibility. infringe or
. M.Sc. Thesis Mark Uitendaal B.Sc.
152 APPENDIXTheE Epicote– System
Mark Uitendaal B.Sc. M.Sc. Thesis
The ETAG data 153 Table 1: the raw ETAG data relative latitude Longitude altitude UTM UTM relative relative time DD,dddd DD,dddd [m] northing Easting position position northing easting ETAG data ETAG
0 67,8933 21,104022 336,6 7530972 504368,6 0 0 – 6 67,898025 21,10782 1989,2 7531499,1 504527,2 527,0614 158,6008 7 67,898705 21,108325 2204,6 7531574,9 504548,3 602,9113 179,6723 8,01 67,89934 21,108783 2415,1 7531645,7 504567,4 673,741 198,792 9,01 67,900005 21,109327 2624,9 7531719,9 504590,1 747,9218 221,4735
20,01 67,921258 21,117517 6546,5 7534090,1 504929,4 3118,081 560,8281 APPENDIX F 21,01 67,924578 21,118628 7125,3 7534460,3 504975,4 3488,316 606,7487 28,02 67,940813 21,125317 9708,6 7536270,9 505252,2 5298,91 883,5937 29,02 67,942792 21,126117 10000,5 7536491,5 505285,3 5519,542 916,6729 30,02 67,944737 21,126855 10288,8 7536708,5 505315,8 5736,454 947,1699 31,02 67,946658 21,127512 10571,5 7536922,8 505342,9 5950,758 974,2453 31,02 67,946658 21,127512 10571,5 7536922,8 505342,9 5950,758 974,2453 39,03 67,959042 21,133003 11832,7 7538303,9 505570 7331,864 1201,381 40,03 67,960512 21,133653 11961,7 7538467,8 505596,9 7495,813 1228,247 41,03 67,961977 21,1343 12086,7 7538631,2 505623,6 7659,205 1254,972 42,03 67,963443 21,134953 12207,3 7538794,8 505650,6 7822,784 1281,973 43,03 67,964918 21,135662 12329 7538959,3 505679,9 7987,297 1311,27
44,03 67,966377 21,136392 12444,2 7539122 505710,1 8149,955 1341,475 50,03 67,974418 21,139745 12513 7540018,8 505848,5 9046,837 1479,836 51,03 67,97575 21,140353 12525,8 7540167,4 505873,6 9195,363 1504,958 52,03 67,977065 21,140968 12537,3 7540314 505899 9342,032 1530,361 53,03 67,978363 21,141572 12545,2 7540458,8 505923,9 9486,842 1555,276 54,04 67,979648 21,142172 12550,3 7540602,2 505948,7 9630,165 1580,053 95,04 67,980925 21,142772 12551 7540744,6 505973,4 9772,559 1604,829 98,04 67,984693 21,14457 12515,2 7541164,9 506047,7 10192,87 1679,087 99,04 67,98591 21,145157 12511,3 7541300,6 506071,9 10328,57 1703,31 100,04 67,987117 21,145727 12496 7541435,2 506095,5 10463,16 1726,836 101,04 67,988312 21,146275 12471,9 7541568,5 506118,1 10596,45 1749,456 102,04 67,989483 21,146833 12455,4 7541699,1 506141,1 10727,13 1772,499 103,04 67,990642 21,1474 12437 7541828,3 506164,5 10856,33 1795,891 104,04 67,99178 21,14797 12418,3 7541955,3 506188 10983,3 1819,425 105,04 67,992907 21,148543 12390,2 7542081 506211,7 11108,97 1843,1 105,04 67,992907 21,148543 12390,2 7542081 506211,7 11108,97 1843,1 112,05 68,000948 21,152105 10480,1 7542977,9 506358,5 12005,91 1989,833 114,05 68,003003 21,153128 10108 7543207,1 506400,7 12235,13 2032,044 115,05 68,004003 21,153627 9914,9 7543318,7 506421,2 12346,67 2052,596 117,05 68,005948 21,15465 9513,4 7543535,6 506463,4 12563,62 2094,826 118,05 68,006897 21,155143 9310,4 7543641,4 506483,8 12669,41 2115,179 119,05 68,007822 21,155603 9104,9 7543744,6 506502,8 12772,58 2134,144 120,05 68,008725 21,156023 8898,5 7543845,3 506520,1 12873,34 2151,442 121,05 68,009617 21,156468 8685,6 7543944,8 506538,4 12972,8 2169,786 122,05 68,010482 21,156905 8472,1 7544041,3 506556,4 13069,29 2187,788
. M.Sc. Thesis Mark Uitendaal B.Sc.
123,05 68,01132 21,157357 8251,7 7544134,8 506575 13162,8 2206,424 124,05 68,012167 21,15789 8019,3 7544229,3 506597,1 13257,25 2228,467 125,06 68,013013 21,158418 7792,6 7544323,7 506618,9 13351,71 2250,301 126,06 68,013838 21,158983 7560,2 7544415,8 506642,3 13443,75 2273,67 127,06 68,014657 21,159488 7325,7 7544507 506663,2 13535,04 2294,534 131,06 68,017858 21,161223 6318,4 7544864,2 506734,7 13892,18 2366,087 154 132,06 68,018557 21,161737 6064,1 7544942,1 506755,9 13970,1 2387,327 133,06 68,019143 21,16228 5795,3 7545007,6 506778,5 14035,57 2409,851 APPENDIX F –ETAG data 136,06 68,021033 21,16392 5036,8 7545218,5 506846,4 14246,46 2477,795 138,06 68,022123 21,165015 4522,3 7545340,1 506891,8 14368,11 2523,205 139,06 68,022633 21,16556 4265,2 7545397 506914,4 14425,03 2545,814 140,06 68,023107 21,16611 4006,8 7545449,9 506937,3 14477,87 2568,642 141,07 68,023547 21,166618 3753 7545499 506958,4 14526,98 2589,74 142,07 68,02397 21,1671 3498,1 7545546,2 506978,3 14574,23 2609,727 143,07 68,024395 21,167652 3247,8 7545593,7 507001,3 14621,68 2632,637 144,07 68,024713 21,168188 2994,5 7545629,2 507023,6 14657,23 2654,952 145,07 68,02501 21,168763 2744,5 7545662,4 507047,5 14690,37 2678,874 146,07 68,025307 21,169362 2492,9 7545695,5 507072,4 14723,52 2703,769 147,07 68,025625 21,169918 2244,1 7545731,1 507095,5 14759,07 2726,918 148,07 68,025937 21,170383 2000,3 7545765,9 507114,9 14793,87 2746,239 149,07 68,026235 21,170815 1756,8 7545799,2 507132,8 14827,18 2764,173 150,07 68,0265 21,171175 1508,4 7545828,8 507147,7 14856,77 2779,124 151,07 68,026808 21,171563 1262,1 7545863,2 507163,9 14891,19 2795,244 152,07 68,027142 21,172017 1019,5 7545900,4 507182,7 14928,41 2814,07
Mark Uitendaal B.Sc. M.Sc. Thesis
155
ETAG data ETAG – APPENDIX F APPENDIX F
Figure F.1: The predicted impact point according to Esrange and the groundtrack of the ETAG data.
. M.Sc. Thesis Mark Uitendaal B.Sc.
156 APPENDIX F –ETAG data
Mark Uitendaal B.Sc. M.Sc. Thesis