Senior Design - Final Design Paper

Transcription

1 University of Central Florida From the SelectedWorks of Hardeo Chin Spring April 30, 2017 Senior Design - Final Design Paper Hardeo Chin Available at:

2 This Time, It s Rocket Science Hybrid Rocket Competition Team #GOAT Sponsor: NASA Florida Space Grant Consortium April 21, 2017 Hardeo Chin Michelle Otero Joseph Roomes Valentina Villegas Roman Williams Faculty Advisor: Kurt Stresau Technical Advisor: Kyle Davidson Graduate Student Advisor: Wilmer Flores Department of Mechanical & Aerospace Engineering College of Engineering & Computer Science University of Central Florida

3 Executive Summary The senior design team has prepared several conceptual designs for a highaltitude hybrid model rocket. The hybrid rocket will reach an altitude of at least 1070 m using a solid fuel grain and liquid oxidizer. The hybrid rocket will also achieve all stages of flight and be lightweight. The overall objective of this project is to design, test and, build a hybrid rocket that will achieve all the critical design requirements mentioned herein. All the conceptual designs, analyses, and results will be discussed throughout this document. The rocket was split into two main components, structures and propulsion. This allowed for designs to be tailored for the specific parameters that correspond to each component, and maximize overall performance. 2

4 Table of Contents Executive Summary... 2 Table of Contents... 3 List of Figures... 4 List of Tables... 5 Glossary... 5 Introduction... 6 Project Objectives & Scope... 7 Assessment of Relevant Existing Technologies and Standards... 7 Professional and Societal Considerations System Requirements and Design Constraints System Concept Development Structural Propulsion Design Analysis Open Rocket Analysis Strain Analysis Thrust Analysis Nozzle Analysis Static Testing Final Design and Engineering Specifications System Evaluation Significant Accomplishments and Open Issues Conclusions and Recommendations References Appendix A: Customer Requirements Appendix B: System Evaluation Plan Appendix C: User Manual Appendix E: Expense Report Appendix F: List of Manuals and Other Documents Appendix G: Calibration Curve Appendix H: Design Competencies

5 List of Figures Figure 1: Schematic of Hybrid Rocket 7 Figure 2: Thrust Curve Demonstrating Burn Rate 11 Figure 3: Fin Shapes 18 Figure 4: Schematic of Fin Design. (a) Trapezoid, (b) Clipped Delta 18 Figure 5:Airfoil Shapes 19 Figure 6: Type of Airfoils 21 Figure 7: Nose Cone Design Schematic. (a) ½ Power Series Cone. (b) ¾ PS Nose Cone 21 Figure 8: LV-HAACK Nose Cone Design 22 Figure 9: VK Nose Cone Schematic 22 Figure 10: Nozzle Concept Design 24 Figure 11: Flame snapshot of different materials. (a) ABS, (b) Acrylic, (c) PP 26 Figure 12: Varies Core Grain Shape and Thrust Curve 27 Figure 13: Various Fuel Grain Core Shape. (a) BATES with inner diameter of 12.70mm. (b) Star with side length of 2.92mm. (c) BATES with inner diameter of (d) Star with side length of 3.92mm. 28 Figure 14: Trimetric Section View of BATES/Star Fuel Grain 28 Figure 15: Effect of temperature of T6 Aluminum Graph 29 Figure 16: 1/2Power Series Fiberglass Fuselage Strain Simulation 31 Figure 17: 3/4Power Series Fiberglass Fuselage Strain Simulation 32 Figure 18: Haack Series Fiberglass Fuselage Strain Simulation 32 Figure 19: Von Kármán Fiberglass Fuselage Strain Simulation 33 Figure 20: 1/2 Power Series Blue Tube Fuselage Strain Simulation 33 Figure 21: 3/4 Power Series Blue Tube Fuselage Strain Simulation 34 Figure 22: Haack Series Blue Tube Fuselage Strain Simulation 34 Figure 23: Von Kármán Series Blue Tube Fuselage Strain Simulation 35 Figure 24: Chamber pressure for designed rocket motor 35 Figure 25: Thrust vs Time Graph for PP 36 Figure 26: Chamber Pressure Graph for Acrylic and ABS 36 Figure 27: Thrust vs Time Graph for ABS 37 Figure 28: Thrust vs Time Graph for Acrylic 37 Figure 29 - Stagnation Pressure Contour Plot - AR 4 38 Figure 30 - Mach No. Contour Plot - AR 4 38 Figure 31 : Stagnation Pressure Contour Plot - AR 3 39 Figure 32: Mach No. Contour Plot AR 3 39 Figure 33 : Stagnation Pressure Contour Plot - AR 7 40 Figure 34: Mach No. Contour Plot AR 7 40 Figure 35: Stagnation Pressure Contour Plot - AR Figure 36: Mach No. Contour Plot AR Figure 37: Motor Assembly 44 Figure 38: The figure on the left shows the isometric view of the circular fuel grain. On the right side, the top view of the fuel grain is shown with dimensions. 45 Figure 39: The figure on the left shows the isometric view of the star shape fuel grain. On the right side, the top view of the fuel grain is shown. 45 Figure 40: Nozzle CAD Drawing 46 Figure 41:Open Rocket Simulation 47 Figure 42: Open Rocket Simulation 47 Figure 43: Thrust Curve 48 Figure 44: Thrust Curve for G Figure 45-Nozzle stuck to Fuel Grain 49 Figure 46: Motor Assembly 57 Figure

6 List of Tables Table 1: Critical Performance Parameters 16 Table 2: Component Breakdown 17 Table 3: Properties of Proposed Nozzle Material 24 Glossary ABS = Acrylonitrile Butadiene Styrene Acrylic = Polymethylmethacrylate a = Burn rate coefficient CFD = Computational Fluid Dynamics FT = Force of thrust g = Gravitational constant at Earth s surface GSE= ground system equipment m = Mass Flow Rate M = Mach Number n = Pressure exponent NOS=liquid nitrous oxide P = Pressure Po = Stagnation Pressure r = Burn Rate Sb = Burning Surface Area To = Stagnation Temperature γ = Specific gas constant 5

7 Introduction Hybrid rockets utilize rocket motors which typically contain a solid fuel and either gas or liquid oxidizer. They provide numerous benefits compared to solid and liquid rockets such as being mechanically simpler, having denser fuels, and providing higher specific impulse. Generally, the oxidizer is liquid and fuel is solid because solid oxidizers are dangerous and are lower performing than their liquid counterparts. Hybrid systems avoid the significant hazards of manufacturing, shipping, and handling that solid rocket motors possess. The performance goals of this design are motivated by maximizing altitude through maximizing thrust, minimizing weight, increasing aerodynamic efficiency, and maintaining stability while adhering to a $600 budget. This design seeks to achieve an altitude of ~1070 meters with an impulse of ~150 N s. Due to competition regulations, the designed impulse value must fall within N s. Static motor testing will be conducted to verify the impulse and ensure the safety of the rocket motor. To meet performance goals, this design will integrate all the necessary elements of a rocket to achieve all the stages of rocket flight. When designing a nose cone, resistance to deformation, aerodynamic drag, and ability to eject are important factors to consider. An ABS Von Karman nose cone shape was selected due to those said characteristics. A fuselage must have sufficient material strength, and be lightweight. Blue tube exhibits those properties and is easily acquirable. Clipped delta fins provided the least aerodynamic drag, were the easiest to manufacture, and were therefore chosen. This hybrid rocket motor will utilize a star and circular shaped fuel grain in conjunction with an original nozzle design to maximize impulse and efficiency thus providing a consistent burn rate and complete combustion. When considering fuel options, manufacturing, density, and chamber pressure are critical parameters. During static motor testing, the two experimental fuels grains to be observed are Paraffin Wax and 3D printed ABS plastic. The chamber pressure, thrust, and specific impulse, will be determined experimentally through static motor testing. The motor casing will be prefabricated due to the complexity and time it takes to design combustion chamber. This project will be implemented at the National Aeronautics & Space Administration Florida Space Grant Consortium (NASA FSGC) hybrid rocket competition. The organization of this report includes the introduction, needs analysis, which will identify the types of users and their needs, the technology assessment, will provide relevant background information, system requirements, concept generation, preliminary engineering analysis, concept evaluation plans, future work, conclusions, and appendix. 6

8 Project Objectives & Scope Long Term Objectives: This design will contribute to the discipline of amateur mid-power rocketry by applying the concepts acquired during tenure as aerospace engineering undergraduates. Rocket hobbyists will be able to optimize performance based on data collected on fuel grains, material selection, and altitude reached. Knowledge of different fuel grain shapes, materials, and G-motor altitude optimization will also be added to the wealth of knowledge of the hybrid rocket community. Semester Objectives: To construct a hybrid rocket motor with a specific impulse (Isp) less than or equal to 160 N-s To maximize the average thrust (N) produced by the rocket motor To achieve the desired burn time (s) for maximum altitude, without exceeding the Isp limit To design a rocket with high material strength (MPa) capable of withstanding the forces of launch To design a recovery system with appropriate time delay (s) that ensures a controlled landing To minimize the coefficient of Drag (cd) experienced by the rocket during flight To design and construct a hybrid rocket that achieves maximum altitude (m) or (ft) Assessment of Relevant Existing Technologies and Standards Literature on the key factors of a hybrid rocket such structure materials, rocket combustion, structural design, instrumentation, launch system and landing element were researched. Better understanding of each of the core components and how to amalgamate them will assist in developing a high preforming hybrid rocket as well as aid in achieving a successful flight. The following sections will analyze each major component and explain their role in the performance of a hybrid rocket. Design With the understanding of the aerodynamics forces acting on the rocket, the design concept becomes a crucial component of a rocket. The overall design requires a great deal of consideration regarding sizes, shapes, and construction of the rocket s main components. In this section, the design of the C-D nozzle, Fins, Nose cone, and fuselage will be further discussed. The overall design of a hybrid rocket can be seen in figure 1. Figure 1: Schematic of Hybrid Rocket 7

9 Fuselage The fuselage, or body tube, is the long, hollow cylinder that houses the combustion chamber, oxidizer tank, and other rocket components. The diameter of the fuselage depends greatly on the size of the combustion chamber and oxidizer tank. A stable rocket design ensures that the center of pressure, Cp, is located below the center of gravity, Cg. Likewise, stability can also be increased by positioning the Cg closer to the nose cone. As the diameter of the fuselage increases, the length must also increase to raise the location of the rocket s center of mass. However, a larger fuselage increases surface area, thus, increasing drag. Nose The nose cone serves to increase aerodynamic performance and minimize drag. A rounded curve is best for a subsonic rocket, while a narrower, sharper pointed cone is optimal for supersonic rockets. Parabolic curves can be calculated and analyzed to optimize aerodynamic ability. Fins Fins provide stability and control direction by inducing drag. However, the induced drag affects the rocket s center of pressure, so the fin shape, placement, and size must be considered. First, fins should be evenly sized and either flat and straight, or a symmetric airfoil shape to reduce unwanted spin and increase direction control. Placing the fins lower on the rocket moves the Cp towards the tail, adding stability, but also, increasing drag. Similarly, larger fins increase stability but also add drag towards the back of the rocket. Considering these factors, optimal stability can be achieved by calculating the necessary number of body diameters (cal) between the Cg and Cp. Structure Materials and Machining Techniques The hybrid rocket can be split up into four main components as far as materials are concerned. The four components being: fuselage, nose cone, fins, nozzle. The different materials for each component were compared using two different parameters material strength and weight. Fuselage There are several design decisions that can be made with the fuselage. The material selection is contingent on whether the hybrid rocket will coast in low speed for long or break Mach early on. This will determine the right weight to strength ratio necessary for an extraordinary launch. The materials studied were vulcanized paper (blue tube), Kraft paper, and G10 fiberglass. The strength parameter that was identified for the fuselage was compressive material strength. The Kraft paper is the best material for lightest design having the lowest mass density but it also has the lowest compressive strength so for the medium powered G rated hybrid rocket it wouldn t be the most effective choice for either scenario. The G10 fiberglass is the toughest material available which can allow for the hybrid rocket to reach transonic speeds that can be beneficial to reach maximum altitude. This strength is offset 8

10 by the significant weight that is introduced by using fiberglass The vulcanized fiber or blue tube is a material that finds a balance between high compressive strength and mass density. The is a 40% decrease in weight compared to the fiberglass but also a 60% decrease in strength. The blue tube would function for either scenario but the true benefit would lay in using it for the low speed coast. The material selection of the fuselage will also determine what other structural components need to be added to the rocket. Nose Cone The nose cone is also a crucial component in the material selection process. The nose cone is the part of the rocket that can make a difference in weight and as far as cutting through the air. There were three materials that were studied: polystyrene plastic, balsa wood and G10 fiberglass. Similar to the fuselage the strength parameter used for the nose cone was compressive strength. The nose cone must withstand compressive forces due to the change in altitude and the effects of the change in thrust and weight. It will also be a place to save precious mass for the overall rocket. The G10 fiberglass is the strongest material that can be selected because of the high compressive strength. This is offset as mentioned before by the weight of the fiberglass. The balsa wood introduces an incredible weight saving option by having a minimal mass density but it does have the smallest compressive strength. Having such a potential for weight savings it should still be considered in the selection process. The polystyrene plastic is the material that offers half the weight of the fiberglass with a high compressive strength that would allow for coasting and possibly transonic flight. Fins The fins of the hybrid rocket are crucial for the balance they offer the rocket. Therefore, the material selection for the fins should be taken under careful consideration. There were three materials that were compared: birch aircraft plywood, polystyrene plastic and G10 fiberglass. The strength parameter for the fins is tensile strength because they will experience tensile stress while in flight. The birch plywood has the lowest mass density but also the smallest tensile strength, this means it would be a good candidate for the low speed coast scenario since it offers a 50% reduction in weight with only an 18% reduction in strength compared to the polystyrene plastic. The G10 fiberglass on the other hand offers a 145% increase in strength compared to the plywood and plastic. The hindrance comes with the 50% increase in mass density compared to the polystyrene plastic. Nozzle The most crucial component of the hybrid rocket is the converging diverging nozzle. The nozzle must be able to withstand large compressive stresses because of the high temperature that it will experience from the combustion of the fuel and oxidizer. Therefore, the strength parameter used for the nozzle materials was compressive strength. There were two materials that were compared for the nozzle: graphite and 6061 aluminum alloy. 9

11 The aluminum is 30% denser compared to the graphite. The graphite is only about 30% weaker than the aluminum. The graphite is also much easier to machine than the aluminum as well. The difference in weight in ratio to a small difference in strength makes the graphite the correct choice for the rocket. Machining Techniques The selection of the right material for the rocket will not assure a successful project because the materials needs to be paired with the right machining techniques. The most important being the C-D nozzle which will be made out of graphite. Graphite can be a challenging material to machine because of its brittle nature. The graphite should always be dry before and during machining. This is to avoid the graphite from absorbing liquid coolants and also making an abrasive slurry during machining. When graphite is machined there should be an adequate ventilation system to vent the dust produced. The graphite should be cut with very a sharp tungsten carbide machine so there won t be any edge chipping. This is the most crucial component of the rocket so the proper machining techniques must be followed. There will also be the possibility of adding structural components to the rocket that will need machining. The addition of aluminum bulkheads or nose cone tip can add more structure integrity. Aluminum like graphite has specific machining practices to ensure that the material is used properly. Aluminum should be machined with carbide coated cutters, as well as small diameter cutters work best. While machining aluminum the chips created by the process should be cleared quite often to avoid damage, and the cutter should be lubricated. The correct machining techniques when followed allow for the material to have its maximum strength when used in application. Propellant Materials There are four type of rocket fuel or propellant: solid, liquid, gas and gel. This study will focus on solid propellant. In hybrid rocketry, solid propellant is commonly used in combination with a liquid oxidizer. Solid propellant consist of varies compositions. Single based, double based, triple based and composite. Single, double and triple based propellants usually contain some type of nitrate explosive. Some Composite propellant contains no nitrate and it is usually a mixture of varies hydrocarbon based materials, a combustible binder and an oxidizer. Since hybrid consist of a solid propellant and liquid oxidizer, the solid propellant used contains only fuel composed of hydrocarbons materials. When selecting materials for the fuel grain, the following properties should be considered: 1. High calorific value 2. Moderate ignition temperature 3. Low moisture content 4. Low NOn (nitrate) combustible matter 5. Moderate velocity of combustion 6. Products of combustion not harmful 7. Low cost 8. Easy to transport 9. Combustion should be controllable 10

12 10. No spontaneous combustion 11. Low storage cost 12. Should burn in air with efficiency Propellant Geometry and Casting The shape and size of a propellant grain determines the burn time, amount of gas, and rate produced from the burning propellant and thrust. Common propellant geometry are Bates, C Slot, D Grain, Moon, Star, X Core, Finocyl, Tablet, Pie Segment, anchor and a solid cylinder. The burning rate surface area is dependent on the shape chosen for the fuel grain. The larger the surface area exposed, the sooner the fuel will burn. The fuel materials are combined and formed into a liquid in order to cast them in the proper shape. The commonly used shape for a charge is a cylindrical solid for its ability to burn in a uniform pattern. There are two casting methods, freestanding and case bonded. A freestanding grain is one, which is cast separate from the motor casing and inserted into the motor when the motor is assembled. The grain is not bonded to the casing, which allows combustion gasses to surround the grain and apply pressure upon the grain equally from all directions. A case bonded grain is casted within the motor casing. When a fuel grain is case bonded, it usually has a liner to prevent the casting from burning. Thrust Curve Burning Rate There are three different type of burns that can be accomplished due to the grain shape, being progressive, regressive and neutral. In a progressive burn, the burning surface area increase with time causing for an increasing thrust. This can be easily obtained with a star shape grain. The grain starts burning from the inside, burning from a small surface area to larger surface area. Creating an opposite effect, in a regressive burn, the burning surface area is decreasing over time, thus a decreasing thrust. A regressive burn, burns from the outside of the grain to the inside. An example would be an annulus concentric fuel grain. Lastly, neutral burn is due to a constant burning over a period of time. The thrust level remains the same throughout. A solid cylinder shape grain would be able to produce a neutral burn. Figure 2 demonstrates the thrust curve associated to the burning type. Figure 2: Thrust Curve Demonstrating Burn Rate 11

13 Ignition System After the oxidizer is injected into the fuel grain, there has to be some source of energy to initiate combustion. There are various different type of ignition system available. The most commonly used ignition systems are pyrotechnic or electrical. For this project, an electrical ignition system will be utilized due to stability and reliability. In electrical ignition system, a high voltage electrical circuit is used to create a spark jump across a gap close to ionize electrical energy. With the liquid oxidizer in the facility, the spark causes a combustion. The ignition system brings the energy need to the surface of the propellant to start burning. There are 3 stages: initiator, booster charge and main charge. Motor Codes The motor classes of model rockets can range from A to G. The range letter corresponds to the maximum ISP (specific impulse) of the motor, scaling through the letters from a smallest step of 1.25 N-s and multiplying each next level by 2. The final upper G limit of 160 N-s is reached after 1.25 is multiplied by 2^7, as G is the seventh letter in the alphabet. The main purpose of motor classes is to separate the model rockets into tangible groups which determine maximum performance in ideal conditions. When applied to model rockets, there is a weight limit at the upper end of the G range of 1500 grams. However, considering the project is not limited to the realm of model rocketry, the weight and scale of the rocket body can increase indefinitely- though this is not advised, as it will adversely affect the climbing performance of the rocket against gravity. Several primary factors in the motor may adjust the ISP output number. They include: Fuel Type Fuel Quantity/Grain Config Oxidizer type, Amount (up to a max of 100% fuel burn efficiency) These factors have the potential to contribute to the impulse of the motor and its corresponding power output. However, the factor most responsible for impulse in the hybrid motor is fuel. The chemical makeup of the fuel and the amount of it used plays a large part in the total impulse calculation. As the motor is a hybrid motor and not commercially configured with integrated recovery ejection charge, the ejection charge is not included in the impulse calculation of the motor. There are additional configuration changes which can affect ISP, including fuel grain distribution, gas flow rate, and internal pressure as well as exit velocity. However, these are not nearly as pertinent as the primary elements listed above. Instrumentation Data Acquisition Digital data acquisition is something that is crucial to the scientific portion of our project including data reliability and analysis. Therefore, a robust calculation and acquisition setup will be needed. Data during testing and launch will be acquired via two inputs: the onboard measurement equipment and the ground based measurement suite. 12

14 In flight, necessary onboard measurement includes a certified pressure altimeter to determine maximum altitude for competition placement. In addition, the altimeter may have other capabilities, include an acceleration or G-force meter that programmable to launch the recovery, or another optional gauge for our own research aims. In the testing phase, it will be necessary to create a measurement system capable of measuring the capability and limits of the fuel system. The ground suite accomplishes these goals by providing a stand, necessary testing equipment, and the data-gathering machine to attach it all to. For this measurement system, a software suite such as NI LabView can be utilized to power and accrue data from the available measurement equipment. The available hardware tools include anything available in the lab for student use, however, the most useful devices will measure tensile strain, pressure, with timing and electronic current testers possible for extra data. All are necessary to test the viability of our motor before flight. The software packages will be tailored to gather the correct data for the experiment. They will need to be acquired or otherwise manufactured, checked, and tested before the real-world test phase begins. Simulation Analyzes The ability to use a model rocket simulator to design and simulate flight allows for a more accurate design of the hybrid rocket. There are two model rocket simulators that are on the market: Open Rocket and RockSim. These two simulators vary from their price to what can be accomplished with each. Open Rocket is a simulator that is used by enthusiasts because it is free. It is capable of making fins and nose cones from templates. Open Rocket is capable of six degrees of freedom simulation and automatic design optimization. This makes it the simulator recommended for beginners. RockSim on the other hand is $130 but it has capabilities that Open Rocket does not. RockSim allows for custom fins and nose cone profiles. RockSim also has the capability of dynamic stability in which it can predict how a rocket will fly in any condition especially windy conditions. Both simulators can be used for the purpose of this project to validate the design that is decided on by the group. Recovery System To achieve a successful flight, NEFAR states a rocket must have a successful launch, deployment of recovery system, and a controlled landing. The last two factors rely heavily on the design, integration, and deployment of the rockets recovery system. Achievement of a controlled landing by means of thrust control would require a throttle system, controlled fuel consumption, fuel saving techniques, and active flight control. Integration of these items might over complicate the design and prove to be unfeasible due to budget constraints. Parachute Materials According to NAR, NEFAR, most model and high-powered rockets utilize a deployable parachute for safe recovery. When designing the parachute for recovery, it is 13

15 important to consider the size and materials of the proposed chute. Parachute materials should be light, flexible, and durable enough not to rip or fail during descent. Materials like Mylar, plastic drop cloths, and dry cleaning bags work well because they can easily be folded up and fit into small body tubes. Garbage bags are a cheap and light material that may be substantial for one launch, but have very little reusable value according to Rocketchutes.com. A more common and durable, material used for model and highpowered rockets is nylon, because it s light, durable, and affordable. Nylon chutes can be purchased ready-to-fly, or in full sheets that require shaping and sizing. Parachute Design The size and shape of the rocket parachute is perhaps the most crucial factor of the recovery system design. According to Apogeerockets.com, the chute should be as small as possible to reduce weight, but, more importantly, allow the fastest rate of descent without causing damage to the rocket. Apogeerockets.com also explains how a safe descent velocity, between meters per second, can be achieved utilizing the following design techniques and equations. The first thing is to calculate the area of a round chute. In order to calculate this, the following equation is used. The variables are defined as g = acceleration of gravity m = mass of the rocket (without fuel) ρ = density of air (at sea level) Cd= estimated coefficient of drag V = desired rate of descent With the area of the chute calculated, the diameter of the chute can be computed with the equation seen below. Where S defines the area of the chute Using the equation below, the area for a polygon parachute can be calculated. With n representing the number of sides of the polygon and D for the length of each side of the polygon. Deployment Methods Finally, a repeatable parachute deployment method must be designed to ensure a successful recovery system. Deployment will likely be triggered by an ejection charge that takes place during the rocket s descent. The charge must be strong enough to eject the 14

16 parachute out of the rocket via detachable parts (e.g nose-cone, body tube, etc.) without damaging the chute, or any other parts One method of deployment utilizes electronic devices, such as an altimeter or accelerometer, to trigger the ejection charge. This design would require some hot-wiring within the rocket, as well as devices that would have to survive the ejection charge. Other constraints introduced by this method include electronic failure, device malfunction, and added weight of the devices. Many rocketeers, and apogeerockets.com, describe the use of a rocket-staging method to deploy chutes. For this method, the ejection charge will be triggered by the rocket motor sometime after the oxidizer is depleted. The charge will push back into the rocket (towards the nose-cone), thus, expelling the chute. To protect the parachute from melting, a type recovery wadding must be placed between the chute and the charge. According to curious.astro.cornell.edu, an astronomy forum, this wadding should be non-flammable and can either be constructed, or purchased from a hobby store. Professional and Societal Considerations The technologies developed within this project will greatly contribute to the knowledge database of amateur hybrid rocketry. The fuel and nozzle fabrication will add to rocket hobbyists arsenal of design choices. The fuel designed was highly machineable, and could be 3D-printed. Mid-powered rockets moderately safe given that the appropriate safety precautions are taken. The only drawback is that during burn bans, the rocket cannot be launched. System Requirements and Design Constraints The design of a functional hybrid rocket warrants the definition of system requirements to ensure the successful launch. This section will explore the methods utilized to identify and define user wants and needs, engineering design requirements, and critical performance parameters. The complete Design Specification document can be found in the Appendix A. Key Features The rocket will largely consist of a body tube, nose-cone, fins, a recovery system, and a hybrid motor. Secondary features include the payload, CD nozzle, centering-rings. Selection of materials and design for each of these components is pertinent to the rockets success. Each of these features are characterized by various requirements relating to the overall design of the rocket. Customer Requirements The customer requirements for this project, defined in the Design Specification Document, stem from user needs and competition regulations described NEFAR, the FAA, 15

17 and NAR. Based on the nature of the completion the rocket must achieve maximum altitude in a safe manner. The rocket must utilize a hybrid motor that does not exceed 160 Newton-seconds of thrust. The rocket must also achieve a safe, controlled recovery. This is summary of the main customer requirements; the complete customer requirements are listed in the appendix. Engineering Design Requirements The engineering design requirements are derived from the previously mentioned customer requirements and serve to shape the design process of the hybrid rocket project. In order to achieve maximum altitude, the rocket must maximize thrust, minimize weight maximize stability, and minimize drag. From these four requirements specific design requirements can be derived for the key components of the rocket. An important parameter in rocketry is the thrust-to-weight ratio. To achieve maximum thrust the rocket motor must contain the most efficient fuel grain, a good oxidizer, and a precisely designed CD nozzle. Minimizing weight requires the careful selection of lightweight materials and appropriately sized components. Stability is another important parameter that must be considered to achieve maximum altitude. To achieve stability, the rocket must be balanced in such a way that the center of pressure follows approximately 1 body-diameter behind the center of gravity. This is achieved by analyzing the placement, size and shape of rocket fins, and considering the location of the rockets center of mass. As velocity increases, the drag forces acting on the surface will increase as well. To mitigate this effect, the rocket must be designed with aerodynamic precision and tested via simulation software. For a complete list of the engineering requirements, refer to the Design Specification Document in the appendix. Critical Parameters The critical performance parameters that govern the overall outcome of the hybrid rockets performance are altitude, weight and thrust. These parameters will be thoroughly considered throughout the design stages of this project. Table 1: Critical Performance Parameters Critical Performance Parameters Target Value Altitude 762 ±100m Weight 800±50g Thrust 140 ± 5 N-s 16

18 The above table shows the selected target values for the three critical performance parameters. All features and components will be designed in regards to these selected parameters. System Concept Development The conceptual design was split up into two components structural and propulsion. These two component were then further broken down into sub components which can be seen in table 2. The structural component has 32 different conceptual designs and the propulsion component has 16 different conceptual designs all varying in designs and materials. Table 2: Component Breakdown Fins Structure Fuselage Nose Cone Hybrid Rocket Recovery System Nozzle Propulsion Fuel Grain Motor Casing Ignition System Structural Fins When designing a hybrid rocket it is important to consider the design of the fins that will be mounted to rocket s rear. Fins provide stability by inducing drag towards the trailing edge of the rocket. By adding weight to the end of the rocket, fins affect the rockets center of gravity, Cg, by pulling it closer to rear. The primary function of rocket fins is to adjust the location of the center of pressure, Cp. According to ApogeeRockets.com, a stable rocket is one in which the Cg is located above the Cp. That being said, the shape of the fins must also be considered to ensure the quantity of induced drag maximizes the rocket's stability, without severely affecting performance. From Nakka-Rocketry.com it was determined that the optimal fin shapes for subsonic rockets are the Clipped Delta, Trapezoidal, and Tapered Swept designs, shown in figure 3. The three designs are not identical and each possess their own advantages and disadvantages. During the selection of fin shape it is crucial to consider impact damage, fin damage due to the rocket s impact with the ground. 17

19 Figure 3: Fin Shapes The Figure 4a shows a CAD model of the trapezoid design created using Solidworks. An advantage of the Trapezoidal design is upward-swept trailing that provides protection from impact upon landing. This advantage is present, but less prominent, in the Clipped Delta design, and not present at all in the Tapered Swept Design. Figure 4b demonstrates a CAD model of the Clipped Delta design. (a) (b) Figure 4: Schematic of Fin Design. (a) Trapezoid, (b) Clipped Delta The Tapered Swept design does, however, have the aerodynamic advantage over the other two designs due to its downward sweep angle. The lower trailing edge lowers the rocket s Cp, increasing stability at the cost of impact protection. For a rocket that must be launched numerous times with minimal repair time in-between, the tapered swept design is probably not optimal. The airfoil shape reduces the pressure drag and induced drag on the fins, thus, optimizing the overall performance. The three airfoil shapes illustrated in the figure 5 will be considered for the fin design of this rocket. 18

20 Figure 5:Airfoil Shapes According to Nakka-Rocketry, the optimal airfoil shape for rockets traveling at mostly subsonic speeds is a rounded leading edge and wedge-shaped trailing edge. Finally, a variation for supersonic and subsonic purposes, known as the unsymmetric design, features a chisel-shaped leading and trailing edge. The unique, unsymmetric shape provides an increased lift force on the longer surface of the fin, which causes a slight rotation about the rocket s longitudinal axis. This slight rotation increases stability by eliminating veering due to unbalanced drag forces. Finally, material selection will play a large role in the design of the fins to ensure the rocket is balanced correctly. Although the location of the rocket s Cg depends on other factors, the weight of the fins greatly affects the rocket. Light fins are beneficial in that they reduce overall weight, however, they tend to more susceptible to damage during flight. On the other hand, heavy fins offer strength and rigidity at the cost of an overall lightweight design. The key to selecting an optimal material lies in the ability to maximize strength, but minimize weight. The first material considered for fin construction is Birch Plywood. This plywood has a tensile strength of MPa and mass density of 609 kg/m 3. As discussed previously, birch plywood is an affordable material that is also easy to machine. The second material considered, Carbon Fiber, offers the largest tensile strength of 600 MPa and a very high mass density of 1600 kg/m 3. Carbon Fiber is a strong, lightweight material known for its many applications in high-performance vehicles. Disadvantages of carbon fiber are that it is extremely expensive and tedious to machine. The third and final material considered is G10 Fiberglass. Fiberglass is widely used in rocketry because it provides relatively high tensile strength, 262 MPa, and has the highest mass density, 1799 kg/m 3. Although fiberglass may provide the optimal tensile strength to mass density ratio, it should be noted that fiberglass is also difficult to machine. Fuselage (Body Tube) Perhaps the single most important structural component of any rocket is the fuselage, also called the body tube. The fuselage holds components pertinent to a successful launch, such as the electronics bay, the rocket motor, and the recovery system. The fuselage is, the main structural component of the rocket and serves to hold the entire 19

21 rocket together. That being said, it is crucial to consider which materials should be used for the rocket s fuselage. In rocketry, the use of lightweight materials is beneficial for increasing the potential max altitude of the rocket. However, for certain components, the selected material must also be strong enough to withstand the forces exerted on the rocket during launch, flight, and landing. The strongest of these forces will be the compressive force due to thrust and gravity acting along the rockets longitudinal axis. Similar to the fins, material selection for the body tube is centered around compressive strength and weight reduction. The first material considered, and possibly the best for performance, is G10 Fiberglass. Fiberglass provides an excellent compressive strength of MPa and is still a relatively lightweight material with a mass density of 1799 kg/m 3. Once again, disadvantages of using fiberglass include its slightly more expensive price and its difficulty to machine. A more affordable, and still sufficient, material is Vulcanized Paper, or Blue Tube. According to Apogeeockets.com, Blue Tube is durable and shatterproof and significantly easier to machine than fiberglass. Although Blue Tube has a compressive strength of MPa, about half the strength of fiberglass, it maintains a relatively high mass density of kg/m 3. The main advantages of Blue Tube are its affordability and machinability. Blue tube can be easily cut with a band saw and is strong enough to withstand higher impact than cardboard. This feature is beneficial in the case of recovery system failure and will prevent total destruction upon impact. Nose Cone The nose cone is the first and perhaps the most important point of interaction with the rocket body with the air. It will contact the fluid medium first and direct the air around the rest of the structure as well. There were four different unique cone shapes observed in the research. Cones from the Power and Haack Series were chosen for our simulation testing, due to their superiority in the subsonic region. Figure 6 displays a general result guide for multiple types of airfoils from sub to super-sonic airflow. The icons are labeled from priority level one through four. One represents the lowest drag and highest performance at Mach, two demonstrates slightly unsatisfactory rated performance, three displays quite unsatisfactory performance and high drag; and four represents barely satisfactory performance and the most drag. 20

22 Figure 6: Type of Airfoils The power series was used to create the first two profiles for the nose cones. The same basic exponential equation generates the revolve curve. The equation follows: y= (R(x/L) n ) As the exponent n decreases from a high to a lower numeral, the shape changes from a line to a parabola. In the half power series cone shown in figure 7a, an exponent of 0.5 is used. Accordingly, in the ¾ power series, an exponent of 3/4 is utilized as the exponent illustrated in figure 7b. (a) Figure 7: Nose Cone Design Schematic. (a) ½ Power Series Cone. (b) ¾ PS Nose Cone HAACK SERIES Both LV and LD-HAACK profiles use the same equation to generate their curves. The equation depends on the variables x, L, and theta. (b) Although this is not a basic geometric shape like the power series, this curve is mathematically derived to eliminate aerodynamic drag, being especially effective in the subsonic Mach region. For that reason it is our best choice. Changing a LV-HAACK to a LD-HAACK equation is as simple as changing the C variable in the equation from 1/3 to 0. (C=0) 21

23 Figure 8: LV-HAACK Nose Cone Design As the rocket should stay within the subsonic regime U<Mach 1, this nose cone will perform very well. With zero as C, the final sine cubed is eliminated, minimizing the size of the integer under the exponent. The results can be observed in the two figures shown above. The Von Karman (LD) form of the Haack nose cone will perform the best throughout the supersonic regime, and marginally better in the subsonic. The base of each nose cone will be shrunken to a smaller radius to snugly fit within the body tube. VK nose design is shown in figure 9. Figure 9: VK Nose Cone Schematic The nose section shall be constructed out of plastic, Acrylonitrile Butadiene Styrene (ABS), using an additive manufacturing device. Because of the ease of accuracy and ease of construction, a commercial 3d printer it is good choice for the nose cone construction. After printing the nose cone, the manufacturer will fit, sand and paint the part. Recovery System A successful launch is characterized by the achievement of all five phases of flight: Lift-off, Engine Burnout, Coasting Phase, Apogee/Ejection, and Recovery. The recovery phase relies almost entirely on the success of the parachute ejection system. With that in mind it is important to take careful consideration into the ejection methods and materials used. The materials used for the parachute play a large role in the parachutes effectiveness. Materials for the chute and cord should be durable, lightweight, and flexible to ensure they can fold up for easy storage within the body-tube. Garbage bags and similar thin plastic materials are good selections because they are cheap, easy to cut, and flexible. A slightly more expensive, but better selection is nylon. Nylon is thin, flexible, and more durable than a standard garbage bag. Also, nylon can be purchased as full chutes or in sheets that are easy to cut and customize. The parachute cord connects to the body-tube and nose-cone and serves to ensure all parts of the rocket are returned safely to the ground. Tensile strength and elasticity are the governing factors in selecting the proper material for the cord. The cord should be heat resistant and strong enough to avoid tearing. Elasticity is important because the rocket will experience a jolting motion once the parachute is deployed. A cord with too much elasticity could cause the rocket parts to bounce into each other during 22

24 recovery, causing damage and an unsteady descent. If the cord has too little elasticity, the tension force due to ejection could completely detach the cord, sending the rocket into a free-fall. Kevlar is a sturdy, flame retardant material that meets the required criteria and can be purchased from most hardware stores. The size and shape of the parachute must also be considered to maximize effectiveness. ApogeeRockets.com provides formula s for calculating the necessary size of the rocket s parachute. The formula below can be used to calculate the necessary area, S, where V is the selected safe descent velocity of approximately 15.6 mph. *Circular Parachute Once the area is determined, the diameter, D, of the chute can easily be calculated using the following formula, Upon the selection of a polygon shaped parachute, the area can be calculated using the formula below where n is the number of sides and D is the diameter of the specific shape. Finally, the method of chute ejection is a crucial element of the parachute system. If the ejection charge fails the rocket will gain speed arbitrarily as it descends towards the ground and violently crashes into the earth. On the other hand, an ejection charge that is too powerful could result in damage to both the rocket and the parachute. Black Powder is an explosive material that will provide a safe, sufficient blast to eject the parachute. A black powder (or Pyrodex) pellet will be placed just outside the electronic bay to eject the upper half of the rocket. The detonation will be triggered electronically by the altimeter, then ignited via electronic matches. Propulsion Converging-Diverging Nozzle A converging-diverging (CD) nozzle is a tube shaped like an asymmetric hourglass as shown in figure 10. It is used to accelerate a hot, pressurized gas from subsonic to supersonic flow. The operation of a CD nozzle can be explained by the following relation which has been derived from the conservation equations: dp da = [ γm 2 (1 M 2 ) ] p A 23

25 where M is the Mach number, p is pressure, A is area, and γ is the specific heat ratio. For subsonic flows (M < 1) the coefficient inside the brackets on the right-hand side is positive. This means that the area and pressure change are in the same direction. We also know from Bernoulli s equation that lower pressure results in increased velocity. Therefore, for subsonic flows, decreasing the area will increase the velocity since pressure and area are in the same direction. For supersonic flow (M > 1), the term on the right-hand side becomes negative, meaning the pressure and area will change in opposite directions an increase in pressure will be accompanied by a decrease in area. Since accelerating a flow requires a decrease in pressure, the area must be increased to increase the flow. Simply put, increasing the area will accelerate a supersonic flow. An important ramification to note is a subsonic flow cannot be accelerated to a supersonic flow in a converging nozzle, even if there is a large difference in pressure a CD nozzle must be used. Also, if there is no difference in stagnation pressure and back pressure, no flow will occur. Nozzle Material Figure 10: Nozzle Concept Design The materials considered for the nozzle were graphite and 6061 aluminum alloy. The nozzle must be able to withstand large compressive stresses and high temperatures due to combustion. The table below lists the properties of both materials. Table 3: Properties of Proposed Nozzle Material Graphite 6061 Aluminum Alloy Density (g/cm 3 ) Compressive Strength (MPa) Melting Point (Kelvin) Cost (per kg) $40 $5 Ductility Hardness (MPa) Aluminum is a very light metal, naturally generates a protective oxide coating, is highly resistant to corrosion, is an excellent heat/electricity conductor, and is cheap. However, aluminum has a low melting point and is ductile. For combustion purposes, higher melting points are preferred. With regards to machining aluminum, one of the major failures is the material adhering to the tool cutting edge. This rapidly degrades the cutting ability of the tool until 24

26 it can no longer cut through material. Tool material selection, such as carbide, and tool coating selection are techniques used to reduce occurrence of build-up on the edge. Although diamond coatings work the best for minimizing build-up, there is a considerable cost associated with them. Maximizing space for chip evacuation is another important factor when machining aluminum. Because aluminum is a soft material, the feed rate is usually increased which results in bigger and more chips. In general, sharp cutting edges should always be used to avoid aluminum elongation creating a better surface finish. Graphite is an excellent conductor of heat and electricity. A key property of graphite is its extremely high temperature stability and chemical inertness, making it an ideal candidate for nozzle design. Although aluminum has a higher compressive strength and density, it has almost half the hardness of graphite. Hardness measures how resistant an object is to various kinds of permanent shape change when a compressive force is applied. This means graphite is less likely to experience a shape change when subjected to the high pressures from combustion. However, graphite is very brittle due its weak intermolecular forces. Therefore, if the nozzle were to somehow get ejected from the rocket, it would shatter. Compared to aluminum, machining graphite can be challenging. Certain guidelines must be considered when machining graphite which are described below: The starting raw graphite material should be dry before machining. If exposed to water, an abrasive slurry will form when mixed with the dust dramatically decreasing the tool life. Since graphite is an abrasive material, diamond or carbide tools should be used for cutting. If a cutting tool loses its sharp edge, it will fracture the graphite material. A dull tool pushes the material rather than cuts it. Graphite has great compressive strength, but will fracture if the force is directed out of it. Graphite should be machined at a higher cutting speed, feed speed, and depth of cut There must be adequate ventilation due to the dust particles graphite produces. Graphite dust is electrically conductive and will fill cracks and openings around the machine enclosure. The static electricity will draw dust to the circuit boards and create short circuits this can lead to expensive damage if the machine is not well equipped. A common practice when machining graphite is the Climb Mill technique, or to work from the outside into the material. Propellant Material Polypropylene is created from the distillation of hydrocarbon fuels into lighter groups called fractions. It is used in a variety of applications including packaging for consumer products, plastic parts, and textiles. Polypropylene has difficulty bonding to other surfaces, meaning it does not adhere well to certain glues that may work fine with other plastics. Another aspect of polypropylene is its low density which would help reduce the overall mass of the design. Polypropylene (PP) is difficult to machine because of its low annealing temperature, meaning it deforms under heat. Since polypropylene is a thermoplastic, it can be melted, cooled, and reheated again without significant degradation to its integrity. 25

27 Shrinkage in PP is about 1-2% but varies based on factors such as holding pressure, holding time, melting temperature, mold temperature, and type of additives. Acrylonitrile butadiene styrene (ABS), a thermoplastic polymer, is a terpolymer composed of polybutadiene, styrene and acrylonitrile. It consists largely of styrene followed by acrylonitrile and polybutadiene being the least material present. Both acrylonitrile and polybutadiene provide the toughness and impact resistance of the polymer. ABS is considered flammable when it is exposed to high temperatures, creating intense reducing flames. It has a burn rate of m/s according to the ISO 3795 flammability test. ISO 3795 measure the time or distance a flame propagates through the chosen material once a flame is applied. Due to its characteristics, ABS has desirable fabricating and machining properties. Polymethylmethacrylate known as acrylic is a strong, lightweight thermoplastic. It has a burning rate of m/s. When ignited acrylic forms carbon dioxide, water, carbon monoxide and some low weight compounds. Due to its thermal and physical properties, when burning acrylic flame is a slow burning blue yellow flame. (a) (b) (c) Figure 11: Flame snapshot of different materials. (a) ABS, (b) Acrylic, (c) PP Figure 11 illustrates the different flame behaviors of each material. ABS demonstrates a strong white yellow flame. This demonstrates the high heat combustion. The flame is laminar, thus a more stable flame reaction. Acrylic demonstrates a stable laminar flame as well. The burning flame is a slow burning blue yellow flame, showing a higher oxygen level in the flame combustion. PP contains a slow burning blue yellow flame like acrylic. When burned, PP creates plastic drips. Propellant Geometry 26

28 The shape of the propellant is critical to the operation of the rocket. The efficiency of the fuel burned will depend on the shape of the fuel grains and the amount of burning surface area exposed. The rate at which the surface burns is referred to as the burning rate and it burns normal to the surface. To compute the burn rate of a grain, the following equation can be utilized: r = ap n, where r is the burn rate, a is the burn rate coefficient, p is the pressure and n is the pressure exponent. Values of both a and n are experimental values, they cannot be theoretically calculated. Various factors play a role in the burn rate of the propellant aside from the shape of the grain. Some key factors are the combustion chamber pressure, the local static pressure, the velocity the combustion gases exhaust and the initial temperature of the grain. Commonly, propellant grains are cylindrical in shape to properly fit in the rocket motor and maximize volumetric efficiency. A central core is created in the propellant segment to increase the surface area exposed to combustion initially 1. The core cross section varies and includes, circular, cross, wagon- wheel, C shaped, D Shaped and dog-bone. As mentioned in the technology assessment, the core shape influences the thrust time profile of the rocket. The different shapes and associated thrust can be seen in figure 12. Figure 12: Varies Core Grain Shape and Thrust Curve After an extensive investigation in the behavior of the fuel burning and the grain shape, the shapes chosen for further investigation were the BATES and star. Both geometries can produce progressive and neutral burn depending on the inhibitors used. The performance of a star shape grain depends on the star shape itself. A star grain with horizontal top edges can produce a neutral burn thus create a constant thrust while a common star with pointed top edges will induce either a regressive or progressive burn. Using BurnSim, the shape, dimension and arrangement of the fuel grain was examined to find the optimal configuration for future study. The propellant segment will be 120 mm in length and 25.4 mm in diameter. Figure 13 demonstrates the various grain core shape to be further tested. When Comparing the circular and star core shape based on burning surface area, the star would perform higher because of the larger Sb. 27

29 (a) (b) (c) (d) Figure 13: Various Fuel Grain Core Shape. (a) BATES with inner diameter of 12.70mm. (b) Star with side length of 2.92mm. (c) BATES with inner diameter of (d) Star with side length of 3.92mm. The dimensions chosen for the core shapes is based on machinability such as common diameter sizes. An additional interested configuration for the fuel grain is a BATES/Star fuel grain. Incorporating both shapes will allow for a progressive burn in addition to a neutral burn. Figure 14, demonstrates the section view of the BATES/Star fuel grain. Figure 14: Trimetric Section View of BATES/Star Fuel Grain Motor Casing For the scope of the design, the motor casing will be pre-fabricated due to the complexity in designing a combustion chamber. The G100 hybrid motor which has a diameter of 38 mm, a length of mm, and mm injector diameter will be acquired 28

30 % of Yield Strength from the Contrail Rockets website. The design pressure of the N2O is ~5157 kpa. Using the following equations below: P D = 2tσ y, P D o s U = 2σ UTS β D where t is the thickness, sd is the design safety factor, σy is the yield strength, σuts is the ultimate strength, Do is the outer diameter of the motor casing, and β is the ratio of yield and ultimate strength (σy/σuts), the design pressure (PD) and burst pressure (PU) were calculated. The design pressure can be thought of as the maximum expected operating pressure the pressure not normally expected to be exceeded during the operation of the motor. The burst pressure is the chamber pressure at which the casing is likely to catastrophically fail. Since motor casing will be comprised of 6061-T6 aluminum alloy, the design pressure and burst pressure were calculated to be kpa and kpa, respectively, with a safety factor of Although, not noticeable, the motor casing will experience some deformation according to the equations below: ΔD = P 2 DD o 2Et D o (1 υ ), Δc = πδd 2 where E is the modulus of elasticity, and ν is Poisson s Ratio, and ΔD is the change in dimeter. We know from the geometry of a circle that the circumference c is the product of pi and the diameter. There the change in diameter multiplied with pi will result in the change in circumference of the motor casing. Using the previously calculated pressures, ΔD = 0.07 mm and Δc = 0.21 mm. Temperature will also have an effect on the strength of the aluminum motor. Figure 15 below displays the effect of temperature on the yield strength after a half hour of exposure. Figure 15: Effect of temperature of T6 Aluminum Graph Notice that the curve quickly decreases after passing 400 K. Strength reduction is a function of time and temperature, therefore if a material is rapidly heated, the strength reduction will be less pronounced. In the case of this design, the strength reduction will be small due to the ~2 sec burn time of the fuel grain. Ignition System Effect of Temperature on Yield Strength T6 Aluminum 0.5 hr. exposure Temperature (K) 29

31 The ignition system is crucial to the proper start and performance of the rocket motor. The rocket will utilize an electronic ignition system, consisting of a spark plug, wiring and compact power source. Upon activation, charge will run from the battery to the plug through the wiring and heat the spark plug to the point of gas ignition. Design Analysis The various concept designs for the structural and propulsion components were analyzed using different engineering analysis methods. The structural concept designs were analyzed for material strength and aerodynamic properties. The propulsion designs were analyzed for propulsion capabilities such as maximum impulse, thrust, combustion, and Mach number. The analysis results were a crucial element in the selection of the final concept design that will be used. Open Rocket Analysis To calculate the center of pressure (Cp) and center of gravity (Cg), the following equations were used. CP = (C Nα) i x i, CG = d iw i C Nα W Where CNα is the dimensionless coefficient that depends on the geometry, and x is the distance from the reference line to the center of gravity to the corresponding component. For the CG equation, the distance d is measured from the reference line to the cg of the individual component. Instead of calculating the equations by hand, the concept design was replicated in OpenRocket which resulted in Cg = cm, Cp = cm, with a stability margin of 1.41 cal. 30

32 Strain Analysis The material strength of the concept designs was analyzed using a strain analysis simulation in Solidworks. The simulation was a static strain study where each of the eight different concept designs were subjected to a takeoff force. The simulation was designed for the takeoff force to be exerted on the nose cone and redistributed to the rest of the body. This ensures that it is accurately simulating the environment the rocket would be exposed to when launched. The takeoff force that was used was based on the initial launch acceleration. This acceleration would be approximately in the magnitude of 10 G s. This acceleration can be used to find the takeoff thrust the rocket would have. This thrust was determined to be 80 N. This is largest force that the rocket will experience throughout launch. The simulation was done using this force acting on all of the concept designs. The four different nose cone design were paired with the two designs for the fins. This lead to eight main concept designs which were analyzed with different materials for the fuselage. The two materials explored for the fuselage in the simulation were fiberglass and blue tube or vulcanized fiber. The analysis is best broken down into two subgroups, designs with the fiberglass fuselage and designs with blue tube. Each of those groups have all four different types of nose cones. Therefore, each sub group had a total of four different simulations. The sub group with fiberglass fuselages will be discussed first. The first being the design with the ½ power series nose cone illustrated in figure 16. Figure 16: 1/2Power Series Fiberglass Fuselage Strain Simulation This figure shows that the fuselage experienced a small amount of strain in the order of 3.805x10 4 this indicates that the fiberglass body tube would be able to withstand the forces that the rocket experiences in flight. The greatest strain was felt in the interaction between the fuselage and the nose cone. The concept design with the ¾ power series nose cone has similar strain interactions but varying magnitudes when compared to the ½ power series nose cone. The takeoff force was better distributed to the rest of the rocket when looking at the ¾ power series nose cone shown in figure

33 Figure 17: 3/4Power Series Fiberglass Fuselage Strain Simulation The fuselage experienced strain in the magnitude of 2.8x10 4 which is quite larger than the strain felt with the ½ power series nose cone. The greatest displacement of the fuselage was 1.4x10-4 mm and the nose cone experienced a displacement of 1.967x10-4 mm. This is also larger than the displacement of the ½ power series design. The concept design with fiberglass fuselage and a Haack nose cone profile was able to better withstand the takeoff force than the previously mentioned designs. This concept design has significantly smaller strains and displacements than the two power series designs. The strain the fuselage experienced was 2.875x10 4 which is almost 2 order of magnitudes smaller than both power series strains mentioned before. Figure 18: Haack Series Fiberglass Fuselage Strain Simulation The figure shows that the interaction between the nose cone and the fuselage also has a strain of 2.885x10 4 which is very minor. The Von Kármán design fared slightly worse than its counterpart the Haack design because of the slight change in slope of the nose cone. The Von Kármán design has a strain in the fuselage of 4.2x10 4, this is still very minor and improved compared to the power series designs. The strain in the nose cone at the contact point between the nose cone and fuselage was 4.8x10 4 shown in figure

34 Figure 19: Von Kármán Fiberglass Fuselage Strain Simulation The Von Kármán design distributed the takeoff force through the body of the rocket leading to less overall displacement. The nose cone also buckled less than both power series nose cones. The other subgroup that was assessed was designs with blue tube fuselages. The same nose cone profiles were used for these analyses. The blue tube has a lower compressive strength than fiberglass so its expected for there to be an increased strain and displacement for all designs in the sub group. This material was tested because it has a lighter mass density. The first design to be assessed was the ½ power series. The fuselage for this design experienced a strain of 3.88x10 4 shown in figure 20. Figure 20: 1/2 Power Series Blue Tube Fuselage Strain Simulation The largest different between blue tube and fiberglass is that the blue tube is weaker than the nose cone therefore there is no buckling in the nose cone. The buckling actually happens at the bottom of the fuselage. The ¾ power series performed a slightly better than the ½ power series in distributing the takeoff force to the body of the rocket. This means that the strain in the fuselage of the rocket was slightly higher at 4.1x

35 Figure 21: 3/4 Power Series Blue Tube Fuselage Strain Simulation The Haack profile design is an example of the buckling that the blue tube can experience because of the nose cone distributing the force almost completely to the fuselage. The fuselage had the greatest strain towards the bottom where the fuselage interacts with the fins shown in figure 22. Figure 22: Haack Series Blue Tube Fuselage Strain Simulation The average strain in the fuselage was 2.2x10 4 but towards the bottom there are points where the strain value is 1.11x10 4, this clearly shows that the Haack nose cone is distributing the takeoff force at almost 10 times the rate of the power series counterparts. The Von Kármán design fared worse than the Haack at distributing the takeoff force. This lead to less strain on the fuselage and less buckling. 34

36 Chamber pressure (MPa) Figure 23: Von Kármán Series Blue Tube Fuselage Strain Simulation The highest strain felt by the rocket was towards the bottom where it buckled slightly with a value of 2.4x10 4. The strain and displacement analysis showed that the selection of the material for the fuselage is a crucial design decision that must be taken under careful consideration. The profile of the nose cone also is crucial to not just the aerodynamics of the rocket but the material integrity. Both parameters were taken into account when making the selection of the final concept design. Thrust Analysis Using SRX, the thrust curve for the proposed fuel grain material were simulated as well as the chamber pressure of the designed motor in respect to the fuel grain material. Figure 24 demonstrates how the chamber pressure will behave due to burning of PP. The chamber pressure constantly increases reaching a maximum of 1.7 MPa where it has a rapid decrease. 2.0 Chamber Pressure vs Time (PP) Time (sec.) Figure 24: Chamber pressure for designed rocket motor 35

37 Chamber pressure (MPa) Thrust (N.) Figure 25 demonstrates the thrust curve for PP. It illustrates a progressive burn. It has a constant increasing thrust and decreases around 1.5 sec after ignition. Figure 26 represents the chamber pressure for Acrylic and ABS. Since both materials are similar in properties, the motor behaves the same. 60 Thrust vs Time (PP) Time (sec.) Figure 25: Thrust vs Time Graph for PP Chamber Pressure vs Time (Acrylic/ABS) Time (sec.) Figure 26: Chamber Pressure Graph for Acrylic and ABS Figure 27 and Figure 28 show the thrust curve for ABS and Acrylic respectively. The Thrust curve for ABS demonstrates a progressive burn with an increasing thrust reaching a thrust of 160 N and rapidly decreasing. Acrylic behaves similar to ABS as seen in figure

38 Thrust (N.) Thrust (N.) Thrust vs. Time (ABS) Time (sec.) Figure 27: Thrust vs Time Graph for ABS Nozzle Analysis Thrust vs Time (Acrylic) Time (sec.) Figure 28: Thrust vs Time Graph for Acrylic ANSYS Fluent was used to perform computational fluid dynamics on the convergingdiverging nozzle. The flow was treated as isentropic, compressible flow and analyzed as a two-dimensional gas dynamics problem. Graphite was the material of selection for the nozzle due to its high thermal resistance and hardness. The area ratio (AR) was the most important consideration of the nozzle design process, which can be found by: A e A = 1 M 2 [ 2 γ 1 (1 + γ M2 )] The AR corresponds to both a subsonic and supersonic Mach value, in this case, the supersonic value will be considered. The Mach number increases as the AR is increased for supersonic values. γ+1 γ 1 37

39 The nozzle received with the motor kit, which will be called the stock nozzle, was replicated using SOLIDWORKS, and had an AR of 4. Below are the pressure and Mach contours as analyzed in Fluent. Figure 29 - Stagnation Pressure Contour Plot - AR 4 Figure 30 - Mach No. Contour Plot - AR 4 The pressure and Mach contours are both agreeable with theory. The stagnation pressure continuously decreases along the length of a nozzle because the flow is constantly trying to expand to the ambient pressure conditions. It is important to note that the flow in this simulation is under-expanded because the exit pressure is greater than 38

40 the back pressure (Pe > Pb). This means there is a slight decrease in nozzle efficiency. Maximum efficiency is obtained through an ideally expanded flow where Pe = Pb. The Mach contour displays typical behavior of isentropic flow accelerated through a nozzle. Initially the flow starts out as subsonic around M = 0.3 and then gets choked at the throat where M = 1, then speeds up to M = 2.5. The following plots are the stagnation pressure and Mach contours for an AR of 3, 7, and 10. Figure 31 : Stagnation Pressure Contour Plot - AR 3 Figure 32: Mach No. Contour Plot AR 3 39

41 Figure 33 : Stagnation Pressure Contour Plot - AR 7 Figure 34: Mach No. Contour Plot AR 7 40

42 Figure 35: Stagnation Pressure Contour Plot - AR 10 Figure 36: Mach No. Contour Plot AR 10 It is important to notice the Mach number increases as the AR is increased. An AR of 10 results in M = 2.82 whereas an AR of 3 results in M = 2.2. As expected, the flow through all the nozzles is under-expanded because of the short nozzle length. If the nozzles were longer, the flow would have more time to expand to ambient conditions. This case is shown in Figure 33 where Pe is closest to Pamb. The nozzle was purposefully designed with a longer length to allow for more expansion. If this nozzle were to have the 41

43 same length as the others, the Pe would have been between the pressure values of the nozzles with an AR of 4 and 10. The selection of the AR was determined by the expected specific impulse (Isp) which can be found through the following equation: I sp = F T m g where FT is thrust, g is the gravitational constant at Earth s surface, and m is the mass flow rate. Mass flow rate can be calculated with: m = AP o γ γ 1 2(γ 1) M (1 + T o R 2 M2 ) where Po is stagnation pressure, To is the stagnation temperature, R is the universal gas constant, and γ is the specific heat ratio. It is important to note that the mass flow rate reaches its maximum value when M = 1 and then becomes a function of the stagnation pressure and stagnation temperature. This means that increasing Po and decreasing To will increase the mass flow rate. At higher Mach numbers, the temperature is lower and pressure is higher. Therefore, at higher Mach, your Isp will be lower due to a higher mass flow. Lower Isp contributes to a lower burn time which is not ideal for this design. Due to these considerations, the AR of 3 was chosen for the final nozzle configuration. Static Testing The most crucial analysis of the design that was conducted was a static firing of the hybrid motor. The experiment consisted of the hybrid motor being fired attached to a test stand made out of steel and plywood. The hybrid motor was upright and attached to the test stand using an aluminum bracket accompanied by a 20kg load cell. The firing was accomplished by using a ground system equipment. The GSE was comprised of a launch controller, pad module, two sets of control cables and two 12 volt batteries. One set of control cables were connected to the solenoid valve attached to the nitrous tank. The second set was connected to the hybrid motor igniter. The data acquisition system of the experiment was comprised of a 20kg load cell, an instrumentation amplifier, a DAQ and laptop with LabVIEW. The load cell was utilized to sense the voltage difference when the hybrid motor was fired. The voltage difference output of the load cell was too small to be used to acquire data. This lead to the integration of an instrumentation amplifier. The amplifier was comprised of a circuit board with a INA 125 instrumentation amplifier, inputs for the load cell, outputs for the DAQ, and a resistor. Before the amplifier was built the amplification gain was determined to be 200 using the equation below. The G being the gain from the amplifier and RG the resistance. This also determined the resistor needed for the amplifier. G = kΩ R G After the amplifier was built it was connected to the data acquisition system for calibration. The calibration was done by attaching different weights to the load cell and seeing the voltage output of each weight or force. This was used to develop a calibration curve that can be found in Appendix G. This calibration curve would determine the force γ+1 42

44 the hybrid motor would be experiencing during firing. The experiment was completed after having the calibration curve. A detailed test plan for the experiment can be found in Appendix B. Final Design and Engineering Specifications The structural section of the rocket was comprised of a fuselage (body tube), nose cone, four fins, centering rings, motor mount, parachute, and electronics bay. The body tube that was chosen for the final design was 54mm blue tube (vulcanized fiber). The nose cone was chosen to have the Von Karman profile. It was also 3D printed using ABS plastic as it was the easiest way to achieve the perfect profile. The fins had a clipped delta profile and were machined out of aeronautical grade plywood. The fins were 107mm in length with a wing span of 45mm. The fins were also machined to be airfoiled. The centering rings were also machined out of plywood, with an outer diameter of 57mm and an inner diameter of 54mm. The motor mount was made of two Pringles cans that were shaped to the right diameter for the hybrid motor. The parachute was a 30 in nylon round parachute with 10ft parachord for a shock cord. The electronics bay is multiple component system. The electronics bay is the housing the altimeter needs to run accurately and safely inside the rocket. The electrics bay body was a coupler made of a Pringles can cut to 14cm in length and 54mm in diameter with a section of body tube attached to the outside of it. The addition of body tube was to ensure the electronics bay was flush with the rest of the body of the rocket. Inside the body of the electronics bay sat a sled that would have the altimeter and battery. The sled was made from aeronautical grade plywood and laser cut to shape. The sled was 12cm in length with a height of 50mm. The electronics bay was sealed with two bulkheads on either end made out of plywood as well. One bulkhead was secured with epoxy and the other was felt removable. A threaded bolt through the entire length of the bay made it easy to take apart the electronics bay to reach the electronics inside. The threaded bolt was attached to the bulkheads with two stop nuts. To one bulkhead an eye bolt was also attached in order to be able to tie the shock cord for the parachute to the electronics bay. After all of the parts were machined the rocket needed to be assembled. First the body tube needed to be cut to right length of cm, the body tube was then cut to allow for the integration of the electronics bay. Then the fins were attached to the body tube. The profile of clipped delta allowed for the fins to be attached flush with the bottom of the body tube. The fins were attached to the body using epoxy clay. The next component to be integrated into the rocket body were three centering rings, which were attached using liquid epoxy and reinforced with epoxy clay. The centering rings were placed on the bottom half of the rocket body 9 cm apart from each other. The electronics bay was next to be placed into the rocket body. The bottom half of the electronics bay was glued to the bottom part of the body tube. The nose cone was the last component to be integrated, it was glued to the top of the body tube. A bulkhead was attached to the base of the nose cone and reinforced with clay epoxy to ensure the nose cone would be secure. A screw eye was screwed into the bulkhead so that the other side of the shock cord could be secured. The parachute was then placed inside the top part of the body tube and protected with recovery wadding. 43

45 The propulsion section of the rocket consisted of the motor casing, motor mount, and motor itself. Initially, an H70 RATTworks motor casing was selected for use but due to the company being out of business, a G100 motor casing from Contrail Rockets was acquired. The motor casing had a 38-mm diameter, and 406 mm length. Below is a simplified schematic of the assembled motor. Snap Rings Top Vent Bulkhead NOS fill area Injection Bulkhead Figure 37: Motor Assembly Fuel Grain Nozzle Before assembling the motor, O-rings were fastened onto the bulkheads and nozzle so that they would have a secure fit but also can slide out the casing if necessary. Then, a NOS fill line would be attached to the preslok on the injector bulkhead. A pyredex pellet would then be secured onto the ignitor wire via electrical tape. The two lines would be taped together with electrical tape. Next, the ignitor and fill line would be fed through the hole in the fuel grain until the grain is flush with the bulkhead. The injector bulkhead and nozzle assembly would then be coated lightly with grease, then placed into the motor casing as shown above. The two wires would also be fed through the nozzle as it is placed inside, and secured with a snap ring. Lastly, place the top vent bulkhead at the top of the casing and secure it with the other snap ring. As mentioned prior, the fuel grain material chosen was ABS. During preliminary investigation, ABS was chosen due to its cost efficiency and its composition properties. For static testing, two fuel design were tested. After researching the burn rate behavior of the varies fuel grain geometries, the fuel geometries chosen were star and circle. The fuel grain was a 1.33 inch diameter cylinder with a height of 5.5 inches. The ABS fuel grains were printed in the innovation lab at the University of Central Florida. Circular Fuel Grain The circular fuel grain had a smaller concentric circle on the inside of the fuel grain. The diameter of the inner circle was 0.75 inches. The CAD drawing of the fuel grains are shown below. 44

46 Figure 38: The figure on the left shows the isometric view of the circular fuel grain. On the right side, the top view of the fuel grain is shown with dimensions. Star Fuel Grain The star shape fuel grain consisted of a inscribed 8 point star with a radius of 0.75 inches. The diameter of the star was chosen to ensure a proper propagation of the burn of the fuel. in addition, the size of the ignition system was taken in consider to allow for proper placement within the fuel grain. The CAD of the follow grain can be seen below. Figure 39: The figure on the left shows the isometric view of the star shape fuel grain. On the right side, the top view of the fuel grain is shown. 45

47 The final nozzle design had an AR of 3. Below is a CAD drawing: Figure 40: Nozzle CAD Drawing The nozzle was machined and fabricated at the UCF CECS Machine Laboratory. The interior flow path of the nozzle is rounded to help smooth the flow with inlet area Ai = 0.8 in, throat area At = 0.36 in, exit area Ae = 0.62 in, and overall length of 1.1 in. The O-ring bearing around the nozzle was designed with a depth and width of in. The bearing was sanded so that the O-ring would have a more secure fit around the nozzle. System Evaluation Open Rocket Analysis Below are various simulations run in Open Rocket. It is important to note that all simulations were ran with the stock G100 motor. 46

48 Figure 41:Open Rocket Simulation Based on the data curve above, our rocket would be on target to reach an apogee of ~880 meters which is within our engineering specifications. The max Mach number would be approximately M = 0.46 Figure 42: Open Rocket Simulation This graph displays the coordinate locations rocket once it hits the ground. Giving an eastward moving wind results in the rocket landing at a more eastern coordinate. 47

49 Figure 43: Thrust Curve Figure 44: Thrust Curve for G100 The thrust curve above is the provided G100 thrust curve which can be found in on the Contrail Rockets website. The thrust curve as calculated in Open Rocket is shown in 48

50 Figure 44. The thrust curves are almost replicas of one another and serve as verification that the computations were accurate. Static Testing Analysis The most vital system evaluation that was completed was a static firing of the hybrid motor. The experiment consisted of the hybrid motor being fired attached to a test stand. The hybrid motor was attached to the test stand with a 20kg load cell. The firing was accomplished by using a ground system equipment and a data acquisition system. A detailed test plan can be found in Appendix B. Due to unforeseen circumstances the load cell was damaged because of over pressurization of another team s motor. This lead to the team not being able to use the data acquisition system. Therefore, the static firing of the hybrid motor with different fuel grains was done and recorded with a video camera. These videos being the only data that was collected were then analyzed for burn time, and flame length. The videos were analyzed in Fiji ImageJ to determine the flame length and burn time. The length was determined by corresponding the length of the motor casing with the pixel size. All fuel grains were tested with the designed nozzle with an AR of 3. The stock fuel which came with the kit had a flame length of cm and a burn time of 2 seconds. This burn time is much higher than the original burn time of 1.4 seconds which would greatly increase the specific impulse of the motor. The circular ABS fuel had a flame length of cm with a burn time of ~2.5 seconds, and the star-shaped ABS had a flame length of cm with a burn time of ~3 seconds. Though thrust measurements were not able to be acquired due to the broken strain gauge, the ABS fuel accompanied with the AR3 nozzle were successful designs. The AR3 nozzle could extend the amount of burn time of the stock fuel from 1.4 to 2 seconds while only having a small decrease in Mach (from 2.4 to 2.2). This means the rocket would have a larger specific impulse. The larger flame sizes from the ABS fuels indicated a larger amount of thrust being generated. A drawback is that the propulsion design might have been more powerful than a G-Motor. Since the grains were 3D-printed, they could easily be redesigned smaller to fall into the G-Motor category thought more static testing would be needed for verification. Another minor drawback to the ABS is that it would get stuck to the nozzle after a test. To remedy this, grease would be placed around the inlet area of the nozzle so that after testing, the nozzle and ABS would easily split without damage to either component. Figure 45-Nozzle stuck to Fuel Grain 49