4.0 Detailed Design g Payload Vehicle Overview

Transcription

1 Project Bellerophon Detailed Design g Payload Vehicle Overview The launch vehicle carrying the 200 g payload (Fig ) hitches a ride on a balloon up to an altitude of 30 km where the first of three stages is ignited. At 30 km, the rocket launches in a vertical orientation from a gondola that is attached to the balloon. Once the rocket finishes burning the propellant in all three stages, the designed orbit perigee is 486 km. When random uncertainties in vehicle performance characteristics are included in the design (Monte Carlo analysis), the launch vehicle achieves an average perigee of 437 km. Fig : Launch vehicle stack up 200g payload. (Daniel Chua) Author: Amanda Briden

2 Project Bellerophon Launch System Breakdown Gondola and Balloon Components Providing support to the launch vehicle and guidance at take-off, the gondola is an all aluminum structure. To support the launch vehicle there are three equally spaced, horizontally oriented, rings that attach to the launch vehicle s outer structure (Fig ). Also positioned horizontally are a square frame (at the bottom of the gondola) and flange (at the top of the gondola). Connecting these rings and frame are four equally spaced, vertically oriented launch rails that guide the launch vehicle off the gondola at ignition. Fig : Launch vehicle and gondola configuration 200g payload. (CJ Hiu) The gondola is connected to a spherical balloon, filled with helium, made of polyethylene plastic. During flight, the gondola carrying the launch vehicle is suspended below the balloon. We assume that the balloon pops right before the launch vehicle passes through it. As the balloon rises, the gas expands and the balloon is sized to hold the gas at an altitude of up to 30 km. The battery, that powers the communications with the range safety officer on the ground, is Author: Amanda Briden

3 Project Bellerophon 34 attached to the flanges of the gondola. Neither the balloon or gondola are reused. Fig puts the size of these components with respect to the launch vehicle into perspective. Fig : Size comparison of the gondola, launch vehicle, and balloon 200g payload. (CJ Hiu) First Stage Fig is an exploded view of the launch vehicle. A reference table, summarizing the sizing and propulsion information for each stage, is also provided. Please refer back to it while reading the descriptions of each stage. Author: Amanda Briden

4 Project Bellerophon 35 BALLOON STRUCTURE GONDOLA STRUCTURE Features Features Minimum volume: m 3 Dimensions: [3] x [3] x [4] m 3 Maximum volume: 279,950 m 3 Material: Aluminum Minimum diameter: m Thickness: 0.04 m Maximum diameter: m Weight: kg Material: Polyethylene plastic film PROPULSION Gas used: Helium Features Shape: Spherical Propellant type: STRUCTURES Stage 1 H2O2 & HTPB Features Stage 2 HTPB/AP/Al & H2O2 Length: Stage 3 HTPB/AP/AL Stage m Propellant amount: Stage m Stage kg Stage m Stage kg Diameter: Stage kg Stage m Engine type: Stage m Stage 1 Hybrid Stage m Stage 2 Solid Inert mass: [1] Stage 3 Solid Stage kg Thrust: Stage kg Stage N Stage kg Stage N Material: Stage N Stage 1 Al ISP: Stage 2 Al Stage seconds Stage 3 Al Stage seconds Thickness: [2] Stage seconds Stage m Expansion ratio: Stage m Stage 1 60 Stage m Stage 2 60 AVIONICS Stage 3 60 Features NOTES Mass: 1. Inert masses include tank, skirt, and nose cone masses. Stage kg 2. Thickness values pertain to the fuel tanks. Stage kg 3. Gondola square base width and length. Stage kg 4. Gondola height. Total system power: 200 Watts 5. Used for LITVC. [5] Fig : Exploded view of launch vehicle stack up and parameter summary 200g payload. (Stephen Bluestone, Amanda Briden, Nicole Bryan, CJ Hiu, Molly Kane, William Ling,Sarah Shoemaker) Author: Amanda Briden

5 Project Bellerophon 36 A hybrid first stage with a hydroxy-terminated polybutadiene (HTPB) solid fuel and hydrogen peroxide (H 2 O 2 ) liquid oxidizer pairing is pressurized with gaseous nitrogen and provides a thrust of 34 kn. Part of the first stage propellant is tapped off to support the liquid injection thrust vector control (LITVC), which is used to steer the rocket. Made out of light-weight spacegrade aluminum, the structure can withstand a maximum acceleration of 4.54 Gs. The first stage is 70.11% of the launch vehicle s gross liftoff mass (GLOM) and the length of this stage is 6.86 m. Fig is a dimensional drawing of the first stage. Fig : Dimensional drawing of the first stage 200g payload. (Nicole Wilcox) Second Stage The second stage is an ammonium perchlorate (AP), aluminum (Al), and HTPB solid motor with an extra tank of H 2 O 2 to provide fuel for the LITVC. The H 2 O 2 is again pressurized with gaseous nitrogen. This stage imparts a thrust of 8.8 kn. Able to withstand a maximum acceleration of Author: Amanda Briden

6 Project Bellerophon Gs, the second stage is made of space-grade aluminum. A cone truncated in the mid-section is used to connect one stage diameter to the next such that there are no gaps in the structure; this is called a skirt. The most significant part of the avionics package is located on the interior of the skirt connecting the second and third stages. The avionics package located in the skirt includes a battery, telecom, central processing unit (CPU), and CPU equipment. These features increase the avionics mass from the first by a factor of 5, for a total avionics mass on the second stage of 30 kg. The second stage is 27.87% of the launch vehicle s GLOM. This stage is 3.11 m long and a dimensional drawing is shown in Fig Fig : Dimensional drawing of the second stage 200g payload. (Nicole Wilcox) Third Stage Since the avionics is jettisoned along with the second stage at the end of its burn, we spin the third stage of the launch vehicle to maintain stability. The propellant type and structural material Author: Amanda Briden

7 Project Bellerophon 38 are identical to the second stage. The third stage is 2.02% of the launch vehicle s GLOM. Stage three is 1.06 m in length and a dimensional drawing follows in Fig Fig : Dimensional drawing of the third stage 200g payload. (Nicole Wilcox) Nose Cone Component The nose cone protecting the top of the launch vehicle from extreme heating is made of aluminum and titanium. An additional feature of the nose cone is a blunted tip made of titanium, which is a heat resistant material. The nose cone is jettisoned once the vehicle reaches an altitude of 90 km (out of the Earth s atmosphere). The nose cone jettison occurs prior to the separation of the first stage. Author: Amanda Briden

8 Project Bellerophon Mission Requirements Verification What are the chances that we reach an orbit with a periapsis of at least 300 km? There is a 99.99% chance that our launch vehicle reaches a periapsis of 300km. After 10,218 Monte Carlo simulations launch vehicle only fails once (Fig ). We therefore meet the mission requirement of 99.86% success rate, considering only non-catastrophic failures. An average perigee, shown as the peak of the histogram in Fig , of 437 km is achieved number of cases Periapsis altitude(km) Fig : 200g periapsis altitude histogram with std = km and mean = km. (Alfred Lynam) What are the chances of a failure that results in complete loss of mission? Accurately predicting the mission success rate, including failures that result in complete loss of mission, is difficult to do without built and tested hardware. Therefore, we turn to the historical success rates of the Ariane IV, Ariane V, and Pegasus, to predict ours. We use the success pattern of Pegasus as it is the only vehicle is air-launched. We predict a 93.84% success rate, which includes catastrophic failures and is achieved after 24 launches. Author: Amanda Briden

9 Project Bellerophon Mission Timeline - A Launch in the Life of the 200g Payload Launch Vehicle T - 1:35:42 to launch The entire launch system begins its 1 hour and 35 minute ascent to its launch altitude of 30 km. On average, the system drifts 121 km before reaching the launch altitude. Prior to ignition, a range safety officer on the ground checks the status of the launch system and has the authority to proceed with or abort the launch. Fig is a visual representation of the stages of flight described in the timeline. T + 00:00:00 to launch We are go for launch! If all systems are go, the first stage is ignited and the launch vehicle is guided off the gondola via four launch rails. We assume that the balloon pops as the launch vehicle passes through it. Throughout the course of the burn, the position of the launch vehicle is determined at every instant by the control system which follows a near optimal steering law. During the first stage the launch vehicle climbs out of the atmosphere and jettisons the nose cone. T + 00:02:17 First Stage Burn-out Approximately two thirds of the way through the first stage burn, the launch vehicle begins a pitch over maneuver. This initial maneuver is of the same form of that used in the Apollo program. After burning for s and climbing to an altitude of 97.4 km, the first stage separates. T + 00:05:35 Second Stage Burn-out During this phase, the launch vehicle continues to pitch over to burn off velocity in the radial direction. At orbit insertion, radial velocity needs to be zero in order for a circular orbit to be achieved. With the burn duration of s and burn out altitude of 347 km, the second stage separates, jettisoning the bulk of the system s avionics. T + 00:08:56 Third Stage Burn-out We re in orbit! For the duration of the third stage burn, the launch vehicle uses spin stabilization to maintain its orientation and does not require avionics control or LITVC. This means that the vehicle s Author: Amanda Briden

10 Project Bellerophon 41 orientation from the end of the second stage burn through the third is maintained. After a s third stage burn time, the launch vehicle ends its ascent and enters an orbit with a perigee of 437 km. The total mission time is 1.7 hours. Fig : Mission Timeline 200g payload. (Amanda Briden, Kyle Donahue, Jeffrey Stuart) Author: Amanda Briden

11 Project Bellerophon Nominal Trajectory In order for the 200 g launch to be considered successful, the payload must reach an orbit of at least 200 km according to the design parameters. Since the main consideration during this project is cost, it s clear to us that a launch which achieves a nearly circular orbit is required. Upon reaching the required orbit, optimization occurs to refine the orbit to nearly circular conditions. We are able to meet these conditions successfully. Table describes the orbital parameters obtained for the 200g payload launch vehicle. Table Orbit Parameters Variable Value Units Periapsis * km Apoapsis * km Eccentricity Inclination 28.5 deg Semi-Major Axis km Period sec *Values are from the surface of the Earth. The periapsis of the orbit is km, this pariapsis exceeds the design requirements by km. The excess altitude accounts for any errors associated with calculations and allows for a margin of error for unforeseen conditions during flight. The apoapsis for the orbit is km, showing that we achieve a nearly circular orbit. An eccentricity of 0 indicates a perfectly circular orbit and we achieve an eccentricity of The inclination angle indicates the plane of the orbit that the launch vehicle is launching into relative to the equator. We re launching eastward from Kennedy Space Center in Cape Canaveral, FL so our inclination angle is 28.5 degrees. Kennedy is chosen in part to maximize the contribution of ΔV Earth assist (see A.6.2.4) The semi-major axis is the distance from the center of an ellipse (center of the Earth) to the edge of an ellipse, and the semi-major axis for our orbit is km. The period of an orbit is the time it takes for a satellite to make one complete revolution. The period for our orbit is seconds which is about 1 hour and 40 minutes. Author: Scott Breitengross

12 Project Bellerophon 43 The velocity we need to reach orbit is measured in the change of velocity also know as ΔV. Table breaks down the ΔV requirements for the 200 g payload. Table ΔV Breakdown Variable Value Units Percent of Total ΔV total 9313 m/s -- ΔV drag 6 m/s ΔV gravity 1991 m/s ΔV Earth assist 411 m/s ΔV leo 7727 m/s ΔV leo is the velocity requirement to maintain our orbit. ΔV drag refers to the velocity requirement to overcome the effects of air resistance on the launch vehicle as it travel through Earth s atmosphere. The ΔV drag value is low because the launch vehicle is only in Earth s atmosphere for a short period of time. ΔV gravity is the velocity requirement to overcome the effects of gravity on the launch vehicle. ΔV Earth assist is the velocity gained from launching from Kennedy Space Center. ΔV Earth assist is calculated from the latitude of the launch location. ΔV Earth assist is larger the closer to the equation the launch location is. ΔV total is the sum total of ΔV drag,, ΔV leo, ΔV gravity, minus ΔV Earth assist. Author: Scott Breitengross

13 Project Bellerophon 44 Figure shows the entire orbit mentioned above. Figure : Full orbit of 200g payload. (Scott Breitengross) A steering law is developed to determine the nominal trajectory of the launch vehicle. We create and use a linear-tangent steering law for each stage. The linear tangent steering law produces the best trajectory but it is possible to use other steering laws. Since we create a steering law for each stage, the coefficients of the steering law are optimized and defined for each stage. Table shows the coefficients for the steering law. Table Coefficients for Steering Law Variable Value a e-1 b e1 a e-3 b e0 a e-19 b e-1 numbers refer to stage number Author: Scott Breitengross

14 Project Bellerophon 45 The linear-tangent steering law is calculated using Eq. ( ) below. ϕ = tan 1 ( at + b) Eq Where φ is the angle the launch vehicle is at, a and b are the constants mentioned above and t is time in seconds. The constants are determined from the trajectory optimization code. The solution to the linear tangent steering law various throughout the trajectory. Table shows the angles, relative to the horizon, that the launch vehicle is in at the end of each stage. Due to the spin stabilization of the third stage, the third stage is at a constant angle of -25. Table Angles from the Steering Law Variable End of 1 st stage End of 2 nd stage End of 3 rd stage Value Units deg deg deg Angles are the nose pointing based on the horizon Figure showss how the angles for the steering law are defined. Figure : Definition of steering law angles. (Amanda Briden) Where b r is pointing up or towards the sky and b θ is pointing east. Author: Scott Breitengross

15 Project Bellerophon 46 Figure shows the beginning of the orbit from launch Figure : Trajectory part of orbit for 200g payload. (Scott Breitengross) The figure for the trajectory part of the orbit looks the way it does for several reasons. The yellow dot is the launch site on the surface of the Earth, and the start of the red line should not correspond to the dot as we are launching from a balloon with an altitude of 30km. The shape of the trajectory is determined by the steering law which changes the angle. Also, the nominal trajectory for the 200 g case is shown in Figure but it is not necessarily the path the launch vehicle will take. By taking all available data into consideration, we were able to demonstrate that launching a 200 g payload into an orbit with a perigee of at least 300 km is possible. Analysis of all contributions to ΔV shows us what is needed to achieve the mission requirements. We then use this data as an input into the trajectory code which optimizes the trajectory. The optimal trajectory produces a nearly circular orbit well above the mission requirement for perigee while minimizing the cost of the project. Author: Scott Breitengross

16 Project Bellerophon Controlled Trajectory: 200g Payload We are not able to exactly match the designed trajectory due to many factors. The trajectory group models the launch vehicle as a point mass to determine the nominal orbit. To arrive at the controlled trajectory the D&C group models the launch vehicle as a rigid body. Also, the Trajectory group s steering law includes sharp corners which are not physically possible. To keep the launch vehicle under control those corners have to be smoothed out. These factors combine to make the controlled trajectory differ from the nominal one. At orbit insertion, the launch vehicle is at a higher altitude which leads to a more eccentric orbit which is illustrated in the following figures. Fig : Close up view of launch trajectory; designed orbit (red), and actual controlled orbit (yellow) (Mike Walker, Alfred Lynam, and Adam Waite) Author: Albert Chaney

17 Project Bellerophon 48 Fig : Designed orbit (red), and actual controlled orbit (yellow) (Mike Walker, Alfred Lynam, and Adam Waite) Below is a table of the orbital parameters for the orbit we achieve. The value a is the semi-major axis, e is the eccentricity, i is the inclination, Ω is the right ascension of the ascending node, and ω is the argument of periapsis. Table Orbital Elements Variable Value Units Periapsis * km Apoapsis * km a km e i deg Ω deg ω deg Footnotes: * Distance from surface Author: Albert Chaney

18 Project Bellerophon 49 Fig : Ground Track of the controlled portion of the launch (Mike Walker, Alfred Lynam, and Adam Waite) Figure is a ground track for the controlled portion of the launch. Ground tracks are important in the design of ground tracking stations and range safety concerns. The ground track is vital in the mission planning of the launch. Author: Albert Chaney

19 Project Bellerophon Subsystem Details Propulsion The propellants we selected for the 200 gram payload launch vehicle were a hybrid first stage and a solid second and third stage. Our selection process involved the use of an optimization code which gave us the best results for a 200 gram payload launch vehicle. The code gave us a propulsion system described in the following section. The first stage of the launch vehicle uses a hybrid rocket motor, with hydrogen peroxide (H 2 O 2 ) as the oxidizer and hydroxyl terminated polybutadiene (HTPB) as the solid propellant. The H 2 O 2 tank is pressurized using gaseous nitrogen. The nozzle is a 12º conical nozzle with liquid injection thrust vector control (LITVC) attached. The LITVC system is composed of four valves that allow H2O2 to be injected into the nozzle at a 90º angle to the centerline of the nozzle. A schematic of the LITVC can be seen below in Figure Figure LITVC and Nozzle Configuration In Figure , the nozzle is shaded grey and all LITVC components are highlighted in orange. The pipes are run from the H 2 O 2 tank that is used for the hybrid motor, and then is distributed to each valve. The valves are connected to the controller which relays a signal for a Author: Stephan Shurn

20 Project Bellerophon 51 certain valve to open and allow pressurized H 2 O 2 to be injected into the main flow in the nozzle, which produces a side thrust. This side thrust allows for control of the launch vehicle during its ascent. The specifics of the propulsion system can be seen in Table Table g Payload Stage 1 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 2,068,000 Pa Mass Flow Rate kg/s Propellant Mass 1, kg Engine Mass kg Thrust (vac) 34,045.3 N Burn Time s Exit Area m 2 Exit Pressure 2, Pa A conical nozzle was chosen because of the solid particles of propellant that will be coming out of the combustion chamber. The combustion process does not necessarily combust the fuel 100% and these particles can deteriorate a nozzle if it is let s say Bell shaped. Some of our early MAT codes had values based off of a 12 conical nozzle and that is one of the reasons we decided on this cone angle for the final design. Also having a smaller cone angle reduces the divergence loss at the exit of the nozzle. A picture of the nozzle can be seen below in Fig Author: Stephan Shurn

21 Project Bellerophon 52 Figure : Our 12 conical nozzle The second stage of the launch vehicle uses a solid rocket motor, with hydroxyl-terminated polybutadiene/ ammonium perchlorate/ aluminum (HTPB/AP/AL) as the propellant. The nozzle is a 12º conical nozzle with LITVC attached. The LITVC has the same configuration as the first stage, with the exception of the H 2 O 2. Since there is no H 2 O 2 already present due to the solid motor, a pressurized tank is added in a curved configuration sitting beneath the solid motor. The tank wraps around the nozzle and is pressurized with gaseous nitrogen so that the H 2 O 2 can flow into the lines for injection. The specifics of the propulsion system can be seen in Table Table g Payload Stage 2 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 6,000,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass kg Thrust (vac) 8,782.6 N Burn Time s Exit Area m 2 Exit Pressure 11, Pa Author: Stephan Shurn

22 Project Bellerophon 53 The third stage of the launch vehicle uses a solid rocket motor, with hydroxyl-terminated polybutadiene/ ammonium perchlorate/ aluminum (HTPB/AP/AL) as the propellant. The nozzle is a 12º conical shape. The specifics of the propulsion system can be seen in Table Table g Payload Stage 2 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 6,000,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass 8.40 kg Thrust (vac) N Burn Time s Exit Area m 2 Exit Pressure 11, Pa Author: Stephan Shurn

23 Project Bellerophon Aerothermal In our aerodynamic analysis, we use linear perturbation theory to determine the aerodynamic loading on the launch vehicle. Linear perturbation theory is the method in which the pressure over the top and bottom surfaces of the launch vehicle is integrated to solve for the normal and axial force coefficients acting on the launch vehicle. It is valid in the subsonic and supersonic regimes, but falls apart in the transonic regime. For this reason, we have ignored the aerodynamic outputs in the transonic regime and only pay attention to the outputs in the subsonic and supersonic regimes. By integrating the change in pressure around the launch vehicle we are able to solve for bending and pitching moments, drag coefficient, axial forces, normal forces, shear forces, and the center of pressure location. All of these aerodynamic moments, coefficients, and forces are based on the final geometry of the launch vehicle as well as the Mach number, angle of attack, and time spent in the atmosphere. Mach number, variation in angle of attack, use of LITVC, stage separation, as well as wind gusts all have a large impact on the aerodynamic loadings of the launch vehicle. As the launch vehicle makes its way through the atmosphere, the change in density also has a significant effect on the impact of these forces and moments. The results for the variation of bending moment and pitching moment with respect to Mach number at zero degree angle of attack can be found in Figs and respectively. Once the launch vehicle reaches a speed of Mach 4.7, it exits the atmosphere. At this point, the first stage has still not separated; therefore, moments are shown as they act on the entire launch vehicle. Author: Jayme Zott

24 Project Bellerophon Bending Moment (Nm) Mach Fig : Variation of bending moment with respect to Mach number at zero angle of attack. 200g. (Alex Woods, Jayme Zott) Pitching Moment (Nm) Mach Fig : Variation of pitching moment with respect to Mach number at zero angle of attack. 200 g. (Alex Woods, Jayme Zott) The moments presented in Figs and correlate well with the magnitude of moments expected for a launch vehicle of our size and shape. It is important for us to determine Author: Jayme Zott

25 Project Bellerophon 56 these moments because the structures group uses them to determine appropriate materials and thicknesses for the final launch vehicle design. The results for the variation of normal, axial, and shear forces with respect to Mach number at a zero degree angle of attack can be found in Figs , , and respectively. The normal and axial forces are important for the D&C group s analysis. D&C uses the normal and axial forces acting on the launch vehicle to help determine the amount of LITVC needed for control at any given moment in time. The shear force is important for the structures group s analysis. Structures uses the shear force acting on the vehicle to help determine appropriate materials and thicknesses for the final launch vehicles design Normal Force (N) Mach Fig : Variation of normal force with respect to Mach number at zero angle of attack. 200 g. (Alex Woods, Jayme Zott) Author: Jayme Zott

26 Project Bellerophon Axial Force (N) Mach Fig : Variation of axial force with respect to Mach number at zero angle of attack. 200 g. (Alex Woods, Jayme Zott) 50 Shear Force (N) Mach Fig : Variation of shear force with respect to Mach number at zero angle of attack. 200 g. (Alex Woods, Jayme Zott) The variation of C D with Mach number at a constant zero angle of attack is shown in figure Because the diameter of the 200g launch vehicle is quite large, the coefficient of drag C D is also quite large. Author: Jayme Zott

27 Project Bellerophon Cd Mach Fig : Impact of Mach number on C D at zero angle of attack. 200 g. (Alex Woods, Jayme Zott) As previously mentioned, we use the linear perturbation theory to determine all aerodynamic forces, coefficients, and moments, including C D. This method requires complete knowledge of the launch vehicle geometry before any aerodynamic forces, coefficients or moments can be determined. This causes a problem because the trajectory analysis requires use of C D long before the final geometry is determined. Because the C D variation shown in Fig is determined after the final launch vehicle geometry has been designed, it cannot be used in the trajectory analysis. Instead, we use a C D trend based on historical data for the trajectory analysis. 1,2 While this historical C D trend is not based on our own geometry, it is based on successful launch vehicles with geometries similar to our final design. The C D based on historical data at zero angle of attack is shown in the Fig Author: Jayme Zott

28 Project Bellerophon Cd Mach Fig : Impact of Mach number on C D at zero angle of attack based on historical data. 200 g. (Jayme Zott) Given additional time, we could complete a better trajectory analysis by including the correct C D based on the linear perturbation theory into the trajectory code. If we created an intermediate file between the initial propulsion sizing output and the trajectory input, a more accurate C D value could be used within the trajectory code. Fig shows the error caused by the using the C D trend based on historical geometries, rather than the C D determined directly from our own geometry. Author: Jayme Zott

29 Project Bellerophon Cd Cd (historical) Cd (dimensional) Mach Fig : Comparison of C D based on historical data and C D based on dimensional analysis (linear perturbation theory). 200 g. (Jayme Zott) Table Summary of Maximum Aerodynamic Loading 200 g. Aerodynamic Load Subsonic Supersonic Bending Moment [Nm] Pitching Moment [Nm] Normal Force [N] Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag C D Dynamic Pressure [Pa] C D % error [%] (Jayme Zott) References 1 Sutton, George P., and Oscar Biblarz. Rocket Propulsion Elements. New York: John Wiley & Sons, Inc., The Martin Company, The Vanguard Satellite Launching Vehicle, Engineering Report No , April Author: Jayme Zott

30 Project Bellerophon Structures The structural components of the launch vehicle for the 200 g payload design include a gondola structure encasing a three-stage launch vehicle. We decided to create the gondola from aluminum bars of 0.04 m thickness. Aluminum was chosen because of its light weight, low cost, strength, low weight, and ease of manufacturing. Fig Gondola frame for rocket element of launch vehicle of a 200 g payload. (Sarah Shoemaker) For our 200 g payload design the frame of the gondola extends m in height and has a square base with sides of m. Ring diameters are m. We then have a total mass of the gondola to kg. This frame can withstand the approximately 55 kpa of pressure exerted on it by our launch vehicle. The first stage of the rocket is m in length and m in diameter. It is comprised of an engine, oxidizer tank, fuel tank, pressurant tank, inter-tank structure, and avionics equipment. The tanks are all made from aluminum and are of various sizes and thicknesses. An inter-stage skirt connects the first and second stages of the rocket. It maintains a 10 slope from the lower stage to the upper stage. It is also made of aluminum and is reinforced with support stringers and ring supports. The first inter-stage structure is m in length. We take our upper and lower Author: Molly Kane

31 Project Bellerophon 62 diameters from the diameters of the first and second stages. For this design, the maximum diameter is m and the minimum diameter is m. The second stage of the rocket consists of an engine, fuel tank, and avionics equipment. This stage has a diameter of m and a length of m. The fuel tank is also made of aluminum. The alloy Al-7075 makes all of our tanks because of its historical use and very high strength to weight ratio. An inter-stage structure connects the second and third stages of the rocket. This second inter-stage skirt is m in height with diameters ranging from m, maximum, to m, minimum, with a constant slope of 10. The third and final stage of the rocket, itself, reaches m in height and is m in diameter. It is composed of an engine, fuel tank, and avionics equipment. We choose the tank to be constructed from aluminum. The payload sits atop the thirst stage, protected by a titaniumtipped nose cone. The nose cone is a simple cone with a blunted nose, and extends m. The end is made of titanium to protect from heat, and the remainder is made of aluminum. The inert mass breakdowns of components and stages are summarized in the following table. Table : Inert Mass Breakdown of Three-Stage Rocket, 200 g Payload Stage 1 Stage 2 Stage 3 Totals Units Fuel Tank kg Ox Tank kg Pressure Tank kg Engine kg Pressure Addition kg Avionics kg Inter-tank kg Skirt/Nose Cone kg Total kg To determine the length of the first stage we take into consideration the lengths of the fist stage nozzle, engine, fuel tank, oxidizer tank, pressurant tank, inter-tank structure, and first inter-stage Author: Molly Kane

32 Project Bellerophon 63 skirt lengths. For the second stage we do not take the nozzle length into consideration because it rests inside of the inter-stage skirt. We do include the second inter-stage skirt length in the dimensions of the second stage. The third stage, similarly, does not include the nozzle length, but has the addition of the nose cone height. This brings the total height of our rocket to m. The following table shows the specifications of each part and each stage. Table : Dimensions of the Three-Stage Rocket, 200 g Payload Stage 1 Stage 2 Stage 3 Totals Units Nozzle Length m Engine Length m Fuel Tank Length m Fuel Tank Thickness n/a m Ox Tank Length m Ox Tank Thickness n/a m Inter-tank Thickness n/a m Press. Tank Diam m Press. Tank Thick n/a m Nose Cone Length m Diameter n/a m Length of Stage m The connecting inter-stage skirts are designed to meet the requirements of the main parts of the launch vehicle. The slope of 10º was chosen because the closer to vertical they are, the more weight they can withstand. However, they still must provide the transition between the two different diameters. Choosing this low-angled slope gave us more efficient stringers with less material needed for each stringer. Ultimately, this reduced the cost of the stringers. The interstage skirt between stages one and two requires a minimum load bearing of kn. The inter-stage skirt between stages two and three calls for a minimum load bearing capability of kn. The skirts are reinforced with stringers and ring supports, detailed as follows. Author: Molly Kane

33 Project Bellerophon 64 Table : Details of the Interstage Structure, 200 g Payload Stage 1-2 Stage 2-3 Units Vertical Length m Shell Thickness m Mass kg Slope Angle deg No. Stringers Stringer Thickness m Stringer Depth m No. Ring Supports Author: Molly Kane

34 Project Bellerophon Avionics We have three subsystems that comprise the avionics portion of the launch vehicle: telecommunications, power systems and range safety. The telecommunications portion of avionics consists of the equipment the ground stations and vehicle require to communicate between the ground and launch vehicle. The avionics packages are broken up into 2 main locations: those that are placed on the gondola, and those that are placed on the inside of the skirt between the second and final stages. We place a battery and some sensors on the gondola to help eliminate some of the avionics weight from the launch vehicle. Most of our avionics are commercial grade products instead of space grade. The decision to use commercial grade components allows us to cut a lot of the cost usually required for additional testing and safety factors that our mission did not require. When choosing commercial grade products we do not consider if we need radiation hardening for avionics and other space grade requirements. Also, we are not able to tell how the loads from the gravitational forces will impact the accuracy of the electronic components. Most of the avionics package is independent of small changes in the launch vehicle design. This is due to most of our avionics basis on the communication requirements for a vehicle and not physical size dimensions. Since all of our vehicles were following the same rough path and had the same functions there was little need for variations. Therefore our avionics package is the same for all 3 launch vehicles. Author: Danielle Yaple

35 Project Bellerophon Cost Our predicted costs for the launch vehicle carrying the 200 g payload are catalogued in Table Table Complete Cost Breakdown for 200 g Payload Launch Vehicle Item Stage 1 Stage 2 Stage 3 Total Propellant $15,350 $2,833 $186 $18,370 Fuel / Ox $14,650 $2,833 $186 Tubing $ Pressurant $ $24 Engine $679,720 $263,690 $79,930 $1,023,340 LITVC $400 $400 - $800 Balloon Helium $74,905 Material $13,384 Gondola $13,200 Ground Costs Personnel $42,000 Handling $2,000 $8,000 $8,000 $18,000 Tanks $1,372,500 $780,100 $122,800 $2,275,400 Material $2,760 $930 $65 $3,755 Manufacturing $19,603 $9,860 $8,956 $38,419 Welding $2,489 $1,344 $512 Riveting $214 $116 $44 Other $16,900 $8,400 $8,400 Wiring Material $500 Installation $7,500 CPU - $10,000 - $10,000 IMU - $3,300 - $3,300 Sensors $800 Battery - $10,000 - $10,000 Range Safety - $20,000 - $20,000 Ground Tracking - $24,000 - $24,000 Telecom Vehicle $10,000 Ground $10,000 Installation $7,500 Total $3,625,196 Author: Alan Schwing

36 Project Bellerophon kg Payload Vehicle Overview The launch vehicle carrying the 1 kg payload (Fig ) hitches a ride on a balloon up to an altitude of 30 km where the first of three stages is ignited. At 30 km, the rocket launches in a vertical orientation from a gondola that is attached to the balloon. Once the rocket finishes burning the propellant in all three stages, the designed orbit perigee is 367 km. When random uncertainties in vehicle performance characteristics are included in the design (Monte Carlo analysis), the launch vehicle achieves an average perigee of 368 km. Fig : Launch vehicle stack up 1kg payload. (Daniel Chua) Author: Amanda Briden

37 Project Bellerophon Launch System Breakdown Gondola and Balloon Components Providing support to the launch vehicle and guidance at take-off, the gondola is an all aluminum structure. To support the launch vehicle there are three equally spaced, horizontally oriented, rings that attach to the launch vehicle s outer structure (Fig ). Also positioned horizontally are a square frame (at the bottom of the gondola) and flange (at the top of the gondola). Connecting these rings and frame are four equally spaced, vertically oriented launch rails that guide the launch vehicle off the gondola at ignition. Fig : Launch vehicle and gondola configuration 1kg payload. (CJ Hiu) The gondola is connected to a spherical balloon, filled with helium, made of polyethylene plastic. During flight, the gondola carrying the launch vehicle is suspended below the balloon. We assume that the balloon pops right before the launch vehicle passes through it. As the balloon rises, the gas expands and the balloon is sized to hold the gas at an altitude of up to 30 km. The battery, that powers the communications with the range safety officer on the ground, is Author: Amanda Briden

38 Project Bellerophon 69 attached to the flanges of the gondola. Neither the balloon or gondola are reused. Fig puts the size of these components with respect to the launch vehicle into perspective. Fig : Size comparison of the gondola, launch vehicle, and balloon 1kg payload. (CJ Hiu, Sarah Shoemaker) First Stage Fig is an exploded view of the launch vehicle. A reference table, summarizing the sizing and propulsion information for each stage, is also provided. Please referr back to it while reading the descriptions of each stage. Author: Amanda Briden

39 Project Bellerophon 70 BALLOON STRUCTURE GONDOLA STRUCTURE Features Features Minimum volume: 2,197.9 m 3 Dimensions: 1 [3] x1 [3] x3.849 [4] m 3 Maximum volume: 190,040 m 3 Material: Aluminum Minimum diameter: m Thickness: 0.04 m Maximum diameter: m Weight: kg Material: Polyethylene plastic film PROPULSION Gas used: Helium Features Shape: Spherical Propellant type: STRUCTURES Stage 1 H2O2 & HTPB Features Stage 2 HTPB/AP/Al & H2O2 Length: Stage 3 HTPB/AP/Al Stage m Propellant amount: Stage m Stage kg Stage m Stage kg Diameter: Stage kg Stage m Engine type: Stage m Stage 1 Hybrid Stage m Stage 2 Solid Inert Mass: [1] Stage 3 Solid Stage kg Thrust: Stage kg Stage N Stage kg Stage N Material: Stage N Stage 1 Al ISP: Stage 2 Al Stage seconds Stage 3 Al Stage seconds Thickness: [2] Stage seconds Stage m Expansion ratio: Stage m Stage 1 60 Stage m Stage 2 60 AVIONICS Stage 3 60 Features NOTES Mass: 1. Inert masses include tank, skirt, and nose cone masses. Stage kg 2. Thickness values pertain to the fuel tanks. Stage kg 3. Gondola square base width and length. Stage kg 4. Gondola height. Total system power: 200 Watts 5. Used for LITVC. [5] Fig : Exploded view of launch vehicle stack up and and parameter summary 1kg payload. (Stephen Bluestone, Amanda Briden, Nicole Bryan, CJ Hiu, Molly Kane, William Ling, Sarah Shoemaker) Author: Amanda Briden

40 Project Bellerophon 71 A hybrid first stage with a hydroxy-terminated polybutadiene (HTPB) solid fuel and hydrogen peroxide (H 2 O 2 ) liquid oxidizer pairing is pressurized with gaseous nitrogen and provides a thrust of 21 kn. Part of the first stage propellant is tapped off to support the liquid injection thrust vector control (LITVC), which is used to steer the rocket. Made out of light-weight spacegrade aluminum, the structure can withstand a maximum acceleration of 2.86 Gs. The first stage is 70.48% of the launch vehicle s gross liftoff mass (GLOM) and the length of this stage is 5.81 m. Fig is a dimensional drawing of the first stage. Fig : Dimensional drawing of the first stage 1kg payload. (Jesii Doyle) Second Stage The second stage is an ammonium perchlorate (AP), aluminum (Al), and HTPB solid motor with an extra tank of H 2 O 2 to provide fuel for the LITVC. The H 2 O 2 is again pressurized with gaseous nitrogen. This stage imparts a thrust of 6.1 kn. Able to withstand a maximum acceleration of Author: Amanda Briden

41 Project Bellerophon Gs, the second stage is made of space-grade aluminum. A cone truncated in the mid-section is used to connect one stage diameter to the next such that there are no gaps in the structure; this is called a skirt. The most significant part of the avionics package is located on the interior of the skirt connecting the second and third stages. The avionics package located in the skirt includes a battery, telecom, central processing unit (CPU), and CPU equipment. These features increase the avionics mass from the first by a factor of 5, for a total avionics mass on the second stage of 30 kg. The second stage is 25.97% of the launch vehicle s GLOM. This stage is 2.44 m long and a dimensional drawing is shown in Fig Fig : Dimensional drawing of the second stage 1kg payload. (Jesii Doyle) Author: Amanda Briden

42 Project Bellerophon Third Stage Since the avionics is jettisoned along with the second stage at the end of its burn, we spin the third stage of the launch vehicle to maintain stability. The propellant type and structural material are identical to the second stage. The third stage is 3.55% of the launch vehicle s GLOM. Stage three is 1.12 m in length and a dimensional drawing follows in Fig Fig : Dimensional drawing of the third stage 1kg payload. (Jesii Doyle) Nose Cone Component The nose cone protecting the top of the launch vehicle from extreme heating is made of aluminum and titanium. An additional feature of the nose cone is a blunted tip made of titanium, which is a heat resistant material. The nose cone is jettisoned once the vehicle reaches an altitude of 90 km (out of the Earth s atmosphere). The nose cone jettison occurs prior to the separation of the first stage. Author: Amanda Briden

43 Project Bellerophon Mission Requirements Verification What are the chances that we reach an orbit with a periapsis of at least 300 km? There is a 99.99% chance that our launch vehicle reaches a periapsis of 300km. After 10,000 Monte Carlo simulations launch vehicle only fails once (Fig ). We therefore meet the mission requirement of 99.86% success rate, considering only non-catastrophic failures. An average perigee, shown as the peak of the histogram in Fig , of 368 km is achieved number of cases Periapsis altitude(km) Fig : 1kg periapsis altitude histogram with std = km and mean = km. (Alfred Lynam) What are the chances of a failure that results in complete loss of mission? Accurately predicting the mission success rate, including failures that result in complete loss of mission, is difficult to do without built and tested hardware. Therefore, we turn to the historical success rates of the Ariane IV, Ariane V, and Pegasus, to predict ours. We use the success pattern of Pegasus as it is the only vehicle is air-launched. We predict a 93.84% success rate, which includes catastrophic failures and is achieved after 24 launches. Author: Amanda Briden

44 Project Bellerophon Mission Timeline - A Launch in the Life of the 1kg Payload Launch Vehicle T - 1:35:34 to launch The entire launch system begins its 1 hour and 35 minute ascent to its launch altitude of 30 km. On average, the system drifts 120 km before reaching the launch altitude. Prior to ignition, a range safety officer on the ground checks the status of the launch system and has the authority to proceed with or abort the launch. Fig is a visual representation of the stages of flight described in the timeline. T + 00:00:00 to launch We are go for launch! If all systems are go, the first stage is ignited and the launch vehicle is guided off the gondola via four launch rails. We assume that the balloon pops as the launch vehicle passes through it. Throughout the course of the burn, the position of the launch vehicle is determined at every instant by the control system which follows a near optimal steering law. During the first stage the launch vehicle climbs out of the atmosphere and jettisons the nose cone. T + 00:02:20 First Stage Burn-out Approximately two thirds of the way through the first stage burn, the launch vehicle begins a pitch over maneuver. This initial maneuver is of the same form of that used in the Apollo program. After burning for s and climbing to an altitude of 87.4 km, the first stage separates. T + 00:05:20 Second Stage Burn-out During this phase, the launch vehicle continues to pitch over to burn off velocity in the radial direction. At orbit insertion, radial velocity needs to be zero in order for a circular orbit to be achieved. With the burn duration of s and burn out altitude of 257 km, the second stage separates, jettisoning the bulk of the system s avionics. T + 00:08:35 Third Stage Burn-out We re in orbit! For the duration of the third stage burn, the launch vehicle uses spin stabilization to maintain its orientation and does not require avionics control or LITVC. This means that the vehicle s Author: Amanda Briden

45 Project Bellerophon 76 orientation from the end of the second stage burn through the third is maintained. After a s third stage burn time, the launch vehicle ends its ascent and enters an orbit with a perigee of 368 km. The total mission time is 1.7 hours. Fig : Mission Timeline 1kg payload. (Amanda Briden, Kyle Donahue, Jeffrey Stuart) Author: Amanda Briden

46 Project Bellerophon Nominal Trajectory The trajectory given is the best case that coincides with the vehicle designed by the team. The final decision to use a high altitude balloon to launch from proved to be beneficial. A balloon launching configuration reduces the amount of drag from the atmosphere which in turn reduces the ΔV necessary to get into Low Earth Orbit (LEO). Table shows the results of the most pertinent orbit parameters and other data that describes the final orbit and trajectory the vehicle is inserted into. Table Orbit Parameters and Other Important Results Variable Value Units Periapsis * 406 km Apoapsis * 481 km Eccentricity Inclination 28.5 deg Semi-Major Axis 6,819 km Period 5,604 s Footnotes: *Altitudes are from the surface of the Earth. Some special notes about Table need to be stated. The mission requirement is to insert the launch vehicle into a 300 km orbit. Table shows the periapsis of the orbit is well above the requirement. We choose a trajectory that allows for errors that might propagate throughout the flight that lowers the resulting periapsis. An important characteristic is the nominal trajectory is very circular with an eccentricity of Finally, a specific value for the inclination is not requested of the team; therefore the inclination is not of great importance to the resulting orbit. Noted in Table is the ΔV budget necessary for the trajectory. The parameter ΔV total is the amount of ΔV the launch vehicle needs to deliver to obtain the stated orbit. We used the ΔV total to size the vehicle. Author: Allen Guzik

47 Project Bellerophon 78 Table ΔV Breakdown Variable Value Units Percent of Total ΔV total 9,379 m/s -- ΔV drag 6 m/s ΔV gravity 2057 m/s ΔV Earth assist 411 m/s ΔV leo 7727 m/s Figure shows a plot of the resulting trajectory and orbit for the 1 kg payload. Figure : Nominal trajectory and orbit for the 1 kg payload. (Allen Guzik) Besides the resulting ΔV the trajectory predicts, the other important parameter other we require is the steering law coefficients. For D&C analysis we need these values to match the nominal ascending path the trajectory analysis calculates. These steering coefficients are found by optimizing the ending orientation of the vehicle. The orientation is defined by three angles, Ψ 1, Ψ 2, and Ψ 3, where they represent and define the orientation of the vehicle at the end of the first, second, and third stages respectively. Figure depicts how Ψ 1, Ψ 2, and Ψ 3 define the orientation of the vehicle during the flight. Table shows the steering angles defined for the nominal trajectory. Author: Allen Guzik

48 Project Bellerophon 79 Figure : Ψ steering law angle orientation definition. (Amanda Briden) Table Angles from the Steering Law Variable Value End of 1 st stage 30 End of 2 nd stage -10 End of 3 rd stage -10 Units deg deg deg From these steering angles the linear tangent steering law coefficients can be defined. Equation defines the linear tangentt steering law Trajectory uses. ϕ = tan 1 ( at + b) Eq The D&C analysis uses these coefficients to control the launching vehicle. Table shows the coefficients used for our launching scenario. Figure shows a close up, view of the ascending trajectory. Author: Allen Guzik

49 Project Bellerophon 80 Table Coefficients for Steering Law Variable Value Units a e-1 -- b e1 -- a e-3 -- b e0 -- a e b e-1 -- Footnotes: Values are coefficients so no units. Figure : Close up view of the ascending trajectory for the 1kg launch configuration. (Allen Guzik) In conclusion, we are very pleased with the resulting nominal trajectory of the 1 kg launch configuration. Our periapsis is above the required 300km, and the orbit is very circular. The trajectory also allows for error to be tolerable and still meet the required orbit. Author: Allen Guzik

50 Project Bellerophon Controlled Trajectory We are not able to exactly match the designed trajectory due to many factors. The trajectory group models the launch vehicle as a point mass to determine the nominal orbit. To arrive at the controlled trajectory the D&C group models the launch vehicle as a rigid body. Also, the Trajectory group s steering law includes sharp corners which are not physically possible. To keep the launch vehicle under control those corners have to be smoothed out. These factors combine to make the controlled trajectory differ from the nominal one. At orbit insertion, the launch vehicle is at a lower altitude which leads to a more eccentric orbit which is illustrated in the following figures. Fig : Close up view of launch trajectory; designed orbit (red), and actual controlled orbit (yellow) (Mike Walker, Alfred Lynam, and Adam Waite) Author: Albert Chaney

51 Project Bellerophon 82 Fig : Designed orbit (red), and actual controlled orbit (yellow) (Mike Walker, Alfred Lynam, and Adam Waite) Below is a table of the orbital parameters for the orbit we achieve. The value a is the semi-major axis, e is the eccentricity, i is the inclination, Ω is the right ascension of the ascending node, and ω is the argument of periapsis. Table Orbital Elements Variable Value Units Periapsis * km Apoapsis * km a km e i deg Ω deg ω deg Footnotes: * Distance from surface Author: Albert Chaney

52 Project Bellerophon 83 Fig : Ground Track of the controlled portion of the launch (Mike Walker, Alfred Lynam, and Adam Waite) Figure is a ground track for the controlled portion of the launch. Ground tracks are important in the design of ground tracking stations and range safety concerns. The ground track is vital in the mission planning of the launch. Author: Albert Chaney

53 Project Bellerophon Subsystem Details Propulsion The propellants we selected for the 1 kilogram payload launch vehicle were a hybrid first stage and a solid second and third stage. Our selection process involved the use of an optimization code which gave us the best results for a 1 kilogram payload launch vehicle. The code gave us a propulsion system described in the following section. Our launch vehicles first stage consists of a hybrid fuel rocket motor. This fuel consists of hydrogen peroxide as the oxidizer and hydroxyl terminated polybutadiene (HTPB) as the solid propellant. The hydrogen peroxide is first catalyzed and then fed through the grain of the solid fuel where it combusts and travels through the nozzle. The nozzle is a 12 conical nozzle with LITVC attached. The LITVC system is composed of four valves that allow H 2 O 2 to be injected into the nozzle at a 90º angle to the centerline of the nozzle. A schematic of the LITVC can be seen below in Figure Figure : LITVC and Nozzle Configuration Authors: Ricky Hinton, Stephan Shurn

54 Project Bellerophon 85 In Figure , the nozzle is shaded grey and all LITVC components are highlighted in orange. The pipes are run from the H 2 O 2 tank that is used for the hybrid motor, and then is distributed to each valve. The valves are connected to the controller which relays a signal for a certain valve to open and allow pressurized H 2 O 2 to be injected into the main flow in the nozzle, which produces a side thrust. This side thrust allows for control of the launch vehicle during its ascent. There is only one engine for this stage. The specific values for the first stage can be seen below in Table Table kg Payload Stage 1 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 2,068,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass kg Thrust (vac) 21,435.5 N Burn Time s Exit Area m 2 Exit Pressure 2, Pa A conical nozzle was chosen because of the solid particles of propellant that will be coming out of the combustion chamber. The combustion process does not necessarily combust the fuel 100% and these particles can deteriorate a nozzle if it is let s say Bell shaped. Some of our early MAT codes had values based off of a 12 conical nozzle and that is one of the reasons we decided on this cone angle for the final design. Also having a smaller cone angle reduces the divergence loss at the exit of the nozzle. A picture of the nozzle can be seen below in Fig Authors: Ricky Hinton, Stephan Shurn

55 Project Bellerophon 86 Figure : Our 12 conical nozzle For our second stage we chose a solid rocket propellant. The compound for this propellant is Hydroxyl-terminated Polybutadiene/ Ammonium Perchlorate/ Aluminum (HTPB/AP/AL). The nozzle once again is a 12 conical nozzle due to the solid propellant. The LITVC system is attached to the nozzle. The LITVC has the same configuration as the first stage, with the exception of the H 2 O 2. Since there is no H 2 O 2 already present due to the solid motor, a pressurized tank is added in a curved configuration sitting beneath the solid motor. The tank wraps around the nozzle and is pressurized with gaseous nitrogen so that the H 2 O 2 can flow into the lines for injection. There is again only one engine for this stage. Table below shows the specifics for this stage. Table kg Payload Stage 2 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 6,000,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass kg Thrust (vac) 6,052.4 N Burn Time s Exit Area m 2 Exit Pressure 11, Pa Authors: Ricky Hinton, Stephan Shurn

56 Project Bellerophon 87 The third and final stage for this launch vehicle consists of a solid propellant motor. The propellant for this stage once again is Hydroxyl-terminated Polybutadiene/ Ammonium Perchlorate/ Aluminum (HTPB/AP/AL). The nozzle is once again a 12 conical nozzle but does not have LITVC control for this stage. There is a single engine for stage three. The specifics can be seen in Table below for stage three of this one kilogram launch vehicle. Table kg Payload Stage 3 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 6,000,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass 9.53 kg Thrust (vac) N Burn Time s Exit Area m 2 Exit Pressure 11, Pa Authors: Ricky Hinton, Stephan Shurn

57 Project Bellerophon Aerothermal In our aerodynamic analysis, we use linear perturbation theory to determine the aerodynamic loading on the launch vehicle. Linear perturbation theory is the method in which the pressure over the top and bottom surfaces of the launch vehicle is integrated to solve for the normal and axial force coefficients acting on the launch vehicle. It is valid in the subsonic and supersonic regimes, but falls apart in the transonic regime. For this reason, we have ignored the aerodynamic outputs in the transonic regime and only pay attention to the outputs in the subsonic and supersonic regimes. By integrating the change in pressure around the launch vehicle we are able to solve for bending and pitching moments, drag coefficient, axial forces, normal forces, shear forces, and the center of pressure location. All of these aerodynamic moments, coefficients, and forces are based on the final geometry of the launch vehicle as well as the Mach number, angle of attack, and time spent in the atmosphere. Mach number, variation in angle of attack, use of LITVC, stage separation, as well as wind gusts all have a large impact on the aerodynamic loadings of the launch vehicle. As the launch vehicle makes its way through the atmosphere, the change in density also has a significant effect on the impact of these forces and moments. The results for the variation of bending moment and pitching moment with respect to Mach number at zero degree angle of attack can be found in Figs and respectively. Once the launch vehicle reaches a speed of Mach 4.5, it exits the atmosphere. At this point, the first stage has still not separated; therefore, moments are shown as they act on the entire launch vehicle. Author: Jayme Zott

58 Project Bellerophon 89 Bending Moment (Nm) Mach Fig : Variation of bending moment with respect to Mach number at zero angle of attack. 1 Kg. (Alex Woods, Jayme Zott) Pitching Moment (Nm) Mach Fig : Variation of pitching moment with respect to Mach number at zero angle of attack. 1 Kg. (Alex Woods, Jayme Zott) The moments presented in Figs and correlate well with the magnitude of moments expected for a launch vehicle of our size and shape. It is important for us to determine these moments because the structures group uses them to determine appropriate materials and thicknesses for the final launch vehicle design. Author: Jayme Zott

59 Project Bellerophon 90 The results for the variation of normal, axial, and shear forces with respect to Mach number at a zero degree angle of attack can be found in Figs , , and respectively. The normal and axial forces are important for the D&C group s analysis. D&C uses the normal and axial forces acting on the launch vehicle to help determine the amount of LITVC needed for control at any given moment in time. The shear force is important for the structures group s analysis. Structures uses the shear force acting on the vehicle to help determine appropriate materials and thicknesses for the final launch vehicles design Normal Force (N) Mach Fig : Variation of normal force with respect to Mach number at zero angle of attack. 1 Kg. (Alex Woods, Jayme Zott) Author: Jayme Zott

60 Project Bellerophon Axial Force (N) Mach Fig : Variation of axial force with respect to Mach number at zero angle of attack. 1 Kg. (Alex Woods, Jayme Zott) 10 Shear Force (N) Mach Fig : Variation of shear force with respect to Mach number at zero angle of attack. 1 Kg. (Alex Woods, Jayme Zott) Author: Jayme Zott

61 Project Bellerophon 92 The variation of C D with Mach number at a constant zero angle of attack is shown in Fig Because the diameter of the 1 kg launch vehicle is quite large, the coefficient of drag C D is also quite large Cd Mach Fig : Impact of Mach number on C D at zero angle of attack. 1 Kg. (Alex Woods, Jayme Zott) As previously mentioned, we use the linear perturbation theory to determine all aerodynamic forces, coefficients, and moments, including C D. This method requires complete knowledge of the launch vehicle geometry before any aerodynamic forces, coefficients or moments can be determined. This causes a problem because the trajectory analysis requires use of C D long before the final geometry is determined. Because the C D variation shown in Fig is determined after the final launch vehicle geometry has been designed, it cannot be used in the trajectory analysis. Instead, we use a C D trend based on historical data for the trajectory analysis. 1,2 While this historical C D trend is not based on our own geometry, it is based on successful launch vehicles with geometries similar to our final design. The C D based on historical data at zero angle of attack is shown in the Fig Author: Jayme Zott

62 Project Bellerophon Cd Mach Fig : Impact of Mach number on C D at zero angle of attack based on historical data. 1 Kg. (Jayme Zott) Given additional time, we could complete a better trajectory analysis by including the correct C D based on the linear perturbation theory into the trajectory code. If we created an intermediate file between the initial propulsion sizing output and the trajectory input, a more accurate C D value could be used within the trajectory code. Fig shows the error caused by the using the C D trend based on historical geometries, rather than the C D determined directly from our own geometry. Author: Jayme Zott

63 Project Bellerophon Cd Cd (historical) Cd (dimensional) Mach Fig : Comparison of C D based on historical data and C D based on dimensional analysis (linear perturbation theory). 1 Kg. (Alex Woods, Jayme Zott) Table Summary of Maximum Aerodynamic Loading 1 Kg. Aerodynamic Load Subsonic Supersonic Bending Moment [Nm] Pitching Moment [Nm] Normal Force [N] Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag C D Dynamic Pressure [Pa] C D % error [%] (Jayme Zott) References: 1 Sutton, George P., and Oscar Biblarz. Rocket Propulsion Elements. New York: John Wiley & Sons, Inc., The Martin Company, The Vanguard Satellite Launching Vehicle, Engineering Report No , April Author: Jayme Zott

64 Project Bellerophon Structures Our launch vehicle, designed to deliver 1kg of payload into low earth orbit, consists of a threestage rocket lifted to an altitude with a balloon and gondola. Bars of aluminum, 0.04 m thick, provide the necessary strength required for the launch vehicle. This gondola is able to with stand the approximately 31 kpa of pressure from launch. Fig Gondola frame for rocket element of launch vehicle of a 1 kg payload. (Sarah Shoemaker) The gondola is an aluminum frame which extends m in height. We made the base is square in shape with sides of 1.0 m and support ring diameters are m. The total mass of our gondola is then kg. The first stage of our rocket contains an engine, oxidizer tank, fuel tank, pressurant tank, intertank structure, and avionics equipment. This stage is m in length and m in diameter. We make all tanks from aluminum and they are of various sizes and thicknesses. The Al-7075 alloy that we employ is proven historically and also has a very high strength to weight ratio. The second stage is made up of an engine, fuel tank, and avionics equipment. It extends m in length with a constant diameter of m. As with the first stage, the fuel tank is made from aluminum. The third stage is m long and has a diameter of m. This is Author: Molly Kane

65 Project Bellerophon 96 the final stage of the rocket element for the launch vehicle. Above the third stage is a nose cone, m long and made of titanium. It protects the 1 kg payload that sits over the third stage. Inert masses of the components vary between stages as follows. Table : Inert Mass Breakdown of Three-Stage Rocket, 1 kg Payload Stage 1 Stage 2 Stage 3 Totals Units Fuel Tank kg Ox Tank kg Pressure Tank kg Engine kg Pressure Addition kg Avionics kg Inter-tank kg Skirt/Nose Cone kg Total kg Dimensions are shown in the following table. We measured the total length of the rocket to be from the end of the first stage nozzle to the tip of the nose cone. This length is found to be m. Table : Dimensions of the Three-Stage Rocket, 1 kg Payload Stage 1 Stage 2 Stage 3 Totals Units Nozzle Length m Engine Length m Fuel Tank Length m Fuel Tank Thickness m Ox Tank Length m Ox Tank Thickness m Intertank Thickness m Press. Tank Diam m Press. Tank Thick m Nose Cone Length m Diameter m Length of Stage m Inter-stage skirts are required to connect and transition from one stage to another. The two skirts lay between the first and second stages and the second and third stages. The first skirt has Author: Molly Kane

66 Project Bellerophon 97 a vertical height of m at a constant 10 slope. Similarly, the second skirt connects the second and third stages and has a constant 10, but with a vertical height of m. The slope of 10º was chosen because the closer to vertical they are, the more weight they can withstand. However, they still must provide the transition between the two different diameters. Choosing this low-angled slope gave us more efficient stringers with less material needed for each stringer. Ultimately, this reduced the cost of the stringers. The inter-stage skirt between stages one and two requires a minimum load bearing of kn. The inter-stage skirt between stages two and three calls for a minimum load bearing capability of kn. The skirts are reinforced with stringers and ring supports, detailed as follows. Table : Details of the Inter-stage Structure, 1 kg Payload Stage 1-2 Stage 2-3 Units Vertical Length m Shell Thickness m Mass kg Slope Angle deg No. Stringers Stringer Thickness m Stringer Depth m No. Ring Supports Author: Molly Kane

67 Project Bellerophon Avionics We have three subsystems that comprise the avionics portion of the launch vehicle: telecommunications, power systems and range safety. The telecommunications portion of avionics consists of the equipment the ground stations and vehicle require to communicate between the ground and launch vehicle. The avionics packages are broken up into 2 main locations: those that are placed on the gondola, and those that are placed on the inside of the skirt between the second and final stages. We place a battery and some sensors on the gondola to help eliminate some of the avionics weight from the launch vehicle. Most of our avionics are commercial grade products instead of space grade. The decision to use commercial grade components allows us to cut a lot of the cost usually required for additional testing and safety factors that our mission did not require. When choosing commercial grade products we do not consider if we need radiation hardening for avionics and other space grade requirements. Also, we are not able to tell how the loads from the gravitational forces will impact the accuracy of the electronic components. Most of the avionics package is independent of small changes in the launch vehicle design. This is due to most of our avionics basis on the communication requirements for a vehicle and not physical size dimensions. Since all of our vehicles were following the same rough path and had the same functions there was little need for variations. Therefore our avionics package is the same for all 3 launch vehicles. Author: Danielle Yaple

68 Project Bellerophon Cost Our predicted costs for the launch vehicle carrying the 1 kg payload are catalogued in Table Table Complete Cost Breakdown for 1 kg Payload Launch Vehicle Item Stage 1 Stage 2 Stage 3 Total Propellant $10,089 $1,680 $225 $11,994 Fuel / Ox $9,500 $1,680 $225 Tubing $ Pressurant $ $38 Engine $634,090 $209,930 $86,860 $930,880 LITVC $400 $400 - $800 Balloon Helium $53,213 Material $9,200 Gondola $13,200 Ground Costs Personnel $42,000 Handling $2,000 $8,000 $8,000 $18,000 Tanks $1,188,600 $633,100 $149,800 $1,971,500 Material $1,853 $560 $78 $2,490 Manufacturing $14,952 $9,580 $8,992 $33,525 Welding $2,166 $1,087 $545 Riveting $186 $94 $47 Other $12,600 $8,400 $8,400 Wiring Material $500 Installation $7,500 CPU - $10,000 - $10,000 IMU - $3,300 - $3,300 Sensors $800 Battery - $10,000 - $10,000 Range Safety - $20,000 - $20,000 Ground Tracking - $24,000 - $24,000 Telecom Vehicle $10,000 Ground $10,000 Installation $7,500 Total $3,178,447 Author: Alan Schwing

69 Project Bellerophon kg Payload Vehicle Overview The launch vehicle carrying the 5 kg payload (Fig ) hitches a ride on a balloon up to an altitude of 30 km where the first of three stages is ignited. At 30 km, the rocket launches in a vertical orientation from a gondola that is attached to the balloon. Once the rocket finishes burning the propellant in all three stages, the designed orbit perigee is 513 km. When random uncertainties in vehicle performance characteristics are included in the design (Monte Carlo analysis), the launch vehicle achieves an average perigee of 516 km. Fig : Launch vehicle stack up 5kg payload. (Daniel Chua) Author: Amanda Briden

70 Project Bellerophon Launch System Breakdown Gondola and Balloon Components Providing support to the launch vehicle and guidance at take-off, the gondola is an all aluminum structure. To support the launch vehicle there are three equally spaced, horizontally oriented, rings that attach to the launch vehicle s outer structure (Fig ). Also positioned horizontally are a square frame (at the bottom of the gondola) and flange (at the top of the gondola). Connecting these rings and frame are four equally spaced, vertically oriented launch rails that guide the launch vehicle off the gondola at ignition. Fig : Launch vehicle and gondola configuration 5kg payload. (CJ Hiu) The gondola is connected to a spherical balloon, filled with helium, made of polyethylene plastic. During flight, the gondola carrying the launch vehicle is suspended below the balloon. We assume that the balloon pops right before the launch vehicle passes through it. As the balloon rises, the gas expands and the balloon is sized to hold the gas at an altitude of up to 30 km. The battery, that powers the communications with the range safety officer on the ground, is Author: Amanda Briden

71 Project Bellerophon 102 attached to the flanges of the gondola. Neither the balloon or gondola are reused. Fig puts the size of these components with respect to the launch vehicle into perspective. Fig : Size comparison of the gondola, launch vehicle, and balloon 5kg payload. (Jeffrey Stuart) First Stage Fig is an exploded view of the launch vehicle. A reference table, summarizing the sizing and propulsion information for each stage, is also provided. Please referr back to it while reading the descriptions of each stage. Author: Amanda Briden

72 Project Bellerophon 103 BALLOON STRUCTURE GONDOLA STRUCTURE Features Features Minimum volume: 6,894.5 m 3 Dimensions: [3] x [3] x [4] m 3 Maximum volume: 596,130 m 3 Material: Aluminum Minimum diameter: m Thickness: 0.04 m Maximum diameter: m Weight: kg Material: Polyethylene y plastic film PROPULSION Gas used: Helium Features Shape: Spherical Propellant type: STRUCTURES Stage 1 H2O2 & HTPB Features Stage 2 HTPB/AP/Al & H2O2 Length: Stage 3 HTPB/AP/Al Stage m Propellant amount: Stage m Stage kg Stage m Stage kg Diameter: Stage kg Stage m Engine type: Stage m Stage 1 Hybrid Stage m Stage 2 Solid Inert mass: [1] Stage 3 Solid Stage kg Thrust: Stage kg Stage N Stage kg Stage N Material: Stage N Stage 1 Al ISP: Stage 2 Al Stage seconds Stage 3 Al Stage seconds Thickness: [2] Stage seconds Stage m Expansion ratio: Stage m Stage 1 60 Stage m Stage 2 60 AVIONICS Stage 3 60 Features NOTES Mass: 1. Inert masses include tank, skirt, and nose cone masses. Stage kg 2. Thickness values pertain to the fuel tanks. Stage kg 3. Gondola square base width and length. Stage kg 4. Gondola height. Total system power: 200 Watts 5. Used for LITVC. [5] Fig : Exploded view of launch vehicle stack up and parameter summary 5kg payload. (Stephen Bluestone, Amanda Briden, Nicole Bryan, Jeffrey Stuart, Molly Kane, William Ling,Sarah Shoemaker) Author: Amanda Briden

73 Project Bellerophon 104 A hybrid first stage with a hydroxy-terminated polybutadiene (HTPB) solid fuel and hydrogen peroxide (H 2 O 2 ) liquid oxidizer pairing is pressurized with gaseous nitrogen and provides a thrust of 75 kn. Part of the first stage propellant is tapped off to support the liquid injection thrust vector control (LITVC), which is used to steer the rocket. Made out of light-weight spacegrade aluminum, the structure can withstand a maximum acceleration of 3.68 Gs. The first stage is 78.95% of the launch vehicle s gross liftoff mass (GLOM) and the length of this stage is m. Fig is a dimensional drawing of the first stage. Fig : Dimensional drawing of the first stage 5kg payload. (Jesii Doyle) Second Stage The second stage is an ammonium perchlorate (AP), aluminum (Al), and HTPB solid motor with an extra tank of H 2 O 2 to provide fuel for the LITVC. The H 2 O 2 is again pressurized with gaseous nitrogen. This stage imparts a thrust of 15 kn. Able to withstand a maximum acceleration of 5.15 Gs, the second stage is made of space-grade aluminum. A cone truncated in the mid-section Author: Amanda Briden

74 Project Bellerophon 105 is used to connect one stage diameter to the next such that there are no gaps in the structure; this is called a skirt. The most significant part of the avionics package is located on the interior of the skirt connecting the second and third stages. The avionics package located in the skirt includes a battery, telecom, central processing unit (CPU), and CPU equipment. These features increase the avionics mass from the first by a factor of 5, for a total avionics mass on the second stage of 30 kg. The second stage is 20.2% of the launch vehicle s GLOM. This stage is 4 m long and a dimensional drawing is shown in Fig Fig : Dimensional drawing of the second stage 5kg payload. (Jesii Doyle) Third Stage Since the avionics is jettisoned along with the second stage at the end of its burn, we spin the third stage of the launch vehicle to maintain stability. The propellant type and structural material are identical to the second stage. The third stage is 0.85% of the launch vehicle s GLOM. Stage three is 1.07 m in length and a dimensional drawing follows in Fig Author: Amanda Briden

75 Project Bellerophon 106 Fig : Dimensional drawing of the third stage 5kg payload. (Jesii Doyle) Nose Cone Component The nose cone protecting the top of the launch vehicle from extreme heating is made of aluminum and titanium. An additional feature of the nose cone is a blunted tip made of titanium, which is a heat resistant material. The nose cone is jettisoned once the vehicle reaches an altitude of 90 km (out of the Earth s atmosphere). The nose cone jettison occurs prior to the separation of the first stage. Author: Amanda Briden

76 Project Bellerophon Mission Requirements Verification What are the chances that we reach an orbit with a periapsis of at least 300 km? There is a % chance that our launch vehicle reaches a periapsis of 300km. After 10,297 Monte Carlo simulations the launch vehicle never fails (Fig ). We therefore meet the mission requirement of 99.86% success rate, considering only non-catastrophic failures. An average perigee, shown as the peak of the histogram in Fig , of 516 km is achieved number of cases Periapsis altitude(km) Fig : 5kg Periapsis altitude histogram with std km and mean = km. (Alfred Lynam) What are the chances of a failure that results in complete loss of mission? Accurately predicting the mission success rate, including failures that result in complete loss of mission, is difficult to do without built and tested hardware. Therefore, we turn to the historical success rates of the Ariane IV, Ariane V, and Pegasus, to predict ours. We use the success pattern of Pegasus as it is the only vehicle is air-launched. We predict a 93.84% success rate, which includes catastrophic failures and is achieved after 24 launches. Author: Amanda Briden

77 Project Bellerophon Mission Timeline - A Launch in the Life of the 5kg Payload Launch Vehicle T - 1:36:00 to launch The entire launch system begins its 1 hour and 36 minute ascent to its launch altitude of 30 km. On average, the system drifts 121 km before reaching the launch altitude. Prior to ignition, a range safety officer on the ground checks the status of the launch system and has the authority to proceed with or abort the launch. Fig is a visual representation of the stages of flight described in the timeline. T + 00:00:00 to launch We are go for launch! If all systems are go, the first stage is ignited and the launch vehicle is guided off the gondola via four launch rails. We assume that the balloon pops as the launch vehicle passes through it. Throughout the course of the burn, the position of the launch vehicle is determined at every instant by the control system which follows a near optimal steering law. During the first stage the launch vehicle climbs out of the atmosphere and jettisons the nose cone. T + 00:02:55 First Stage Burn-out Approximately two thirds of the way through the first stage burn, the launch vehicle begins a pitch over maneuver. This initial maneuver is of the same form of that used in the Apollo program. After burning for s and climbing to an altitude of 129 km, the first stage separates. T + 00:06:28 Second Stage Burn-out During this phase, the launch vehicle continues to pitch over to burn off velocity in the radial direction. At orbit insertion, radial velocity needs to be zero in order for a circular orbit to be achieved. With the burn duration of 213 s and burn out altitude of 406 km, the second stage separates, jettisoning the bulk of the system s avionics. T + 00:09:26 Third Stage Burn-out We re in orbit! For the duration of the third stage burn, the launch vehicle uses spin stabilization to maintain its orientation and does not require avionics control or LITVC. This means that the vehicle s Author: Amanda Briden

78 Project Bellerophon 109 orientation from the end of the second stage burn through the third is maintained. After a s third stage burn time, the launch vehicle ends its ascent and enters an orbit with a perigee of 516 km. The total mission time is 1.8 hours. Fig : Mission Timeline 5kg payload. (Amanda Briden, Kyle Donahue, Jeffrey Stuart) Author: Amanda Briden

79 Project Bellerophon Nominal Trajectory The nominal trajectory and orbit for the 5 kg payload is directly related to lowering the cost of the launch vehicle. If the launch vehicle does not try to follow a nominal trajectory it will be over designed and over built. The mission requirements for project Bellerophone are to place a 5 kg payload into an orbit with a minimum altitude of 300 km. We meet the requirement of a minimum altitude and create an orbit which is near to circular. The final design uses a balloon as a launch platform which reduces the drag on the launch vehicle and this reduces the total velocity needed to get into Low Earth Orbit (LEO). The following table describes the orbital parameters necessary to understand what orbit this vehicle is in. Table Orbit Parameters Variable Value Units Periapsis * km Apoapsis * km Eccentricity Inclination 28.5 deg Semi-Major km Axis Period sec *Values are from the surface of the Earth. The periapsis of an orbit is closest approach to the surface of the Earth once it is in its orbit. For our vehicle the periapsis is km above the desired altitude. The apoapsis is the furthest distance from the surface of the Earth in which the vehicle will experience. For the mission a given apoapsis was not specified. The eccentricity is a measure on how circular the orbit is. For a circular orbit the eccentricity should be zero. This translates into a constraint on apoapsis, so we have an apoapsis difference of km. Project Bellerophon did not have a specified inclination to the orbit. Since we are launching from the Kennedy Space Center in Cape Canaveral, FL and launching directly east our orbit has an inclination of 28.5 o. The semi-major axis is the distance from the center of the ellipse (center of the Earth) to the edge of the ellipse, and the semi-major Author: Kyle Donahue

80 Project Bellerophon 111 axis for our orbit is km. The period of an orbit is the time it takes for the satellite to make one complete revolution and the period for our orbit is seconds which is about 1 hour and 40 minutes. The velocity needed to reach our orbit is measured in the change of velocity also know as ΔV. Table breaks down the ΔV budget for the 5 kg case of Project Bellerophon. Table ΔV Breakdown Variable Value Units Percent of ΔV total ΔV total 9354 m/s -- ΔV drag 4 m/s ΔV gravity 2034 m/s ΔV Earth assist 411 m/s ΔV leo 7727 m/s The ΔV total is a combination of all the other ΔVs which are: ΔV drag, ΔV gravity, ΔV Earth assist, ΔV leo. ΔV drag refers to the velocity needed to overcome the drag which we will experience. This value seems incredibly low, and it should be that way because we are launching from a balloon at an altitude of 30 km. Since we are launching from so high in the atmosphere the air density is relatively low and does not cause much resistance to the launch vehicle. ΔV gravity is the velocity needed to overcome gravity drag. ΔV Earth assist refers to the velocity the Earth s spin is helping the launch vehicle reach orbit. This is the only ΔV which is helping us, the other ΔVs are velocities we need to overcome. ΔV leo is the velocity needed to achieve our orbit. Author: Kyle Donahue

81 Project Bellerophon 112 Figure shows the entire orbit mentioned above. Fig : Full orbit of 5kg payload. (Kyle Donahue) In order to obtain any orbit a steering law is needed to put the rocket on the correct path. We created and used a linear-tangent steering law for each stage. There are many other types of steering laws besides linear-tangent. Other types of steering laws include linear with any of the trigonometric functions along with polynomial with any of the trigonometric functions. The linear-tangent steering law we used is calculated using Eq. ( ) below. tan 1 ϕ = ( at + b) Eq Where φ is the angle the launch vehicle is at, a is the constant mentioned above, t is time in seconds, and b is the other constant mentioned above. Since we are using a linear-tangent law we have two coefficients for each part of the law. Table has the values of the two coefficients (a and b) for each stage. Author: Kyle Donahue

82 Project Bellerophon 113 Table Coefficients for Steering Law Variable Value a e-1 b e1 a e-3 b e0 a e-19 b e-1 numbers refer to stage number These coefficients stay constant for each stage, but the angles in which they create change over time. In order to better understand the steering law and what the coefficients do Table describess the angles in which the vehicle is pointing at the end of each stage. Table Angles from the Steering Law Variable End of 1 st stage End of 2 nd stage End of 3 rd stage Value Units deg deg deg Angles are the nose pointing based on the horizon The angles in Table referr to the angle at which the nose of the rocket is pointing relative to the horizon. For example if the rocket were pointing directly east and parallell to the surface of the Earth then the angle would be 0 o. Figure shows how the angles for the steering law are defined. Fig : Definition of steering law angles. Author: Kyle Donahue

83 Project Bellerophon 114 (Amanda Briden) Where b r is pointing up or towards the sky and b θ is pointing east. Figure is the trajectory part of the orbit mentioned. Fig : Trajectory part of orbit for 5kg payload. (Kyle Donahue) The yellow dot is the launch site on the surface of the Earth, and the start of the red line should not correspond to that as we are launching from a balloon with an altitude of 30km. The shape of the trajectory is determined by the steering law which changes the angle. The figure shows the nominal trajectory for the rocket but not necessarily the path the rocket will take. The trajectory meets the mission requirement of an orbit with a periapsis altitude of at least 300km. We accomplish our mission using a linear-tangent steering law and launching from a balloon. Author: Kyle Donahue

84 Project Bellerophon Controlled Trajectory We are not able to exactly match the designed trajectory due to many factors. The trajectory group models the launch vehicle as a point mass to determine the nominal orbit. To arrive at the controlled trajectory the D&C group models the launch vehicle as a rigid body. Also, the Trajectory group s steering law includes sharp corners which are not physically possible. To keep the launch vehicle under control those corners have to be smoothed out. These factors combine to make the controlled trajectory differ from the nominal one. At orbit insertion, the launch vehicle is at a lower altitude which leads to a more eccentric orbit which is illustrated in the following figures. Figure : Nominal (red) and controlled (yellow) trajectories, 5 kg (Authors: Mike Walker, Alfred Lynam, Adam Waite) Author: Jeffrey Stuart

85 Project Bellerophon 116 Figure : Nominal (red) and controlled (yellow) orbits, 5 kg (Authors: Mike Walker, Alfred Lynam, Adam Waite) Below is a table of the orbital parameters for the orbit we achieve. The value a is the semi-major axis, e is the eccentricity, i is the inclination, Ω is the right ascension of the ascending node, and ω is the argument of periapsis. Table Orbital Elements Variable Value Units Periapsis * km Apoapsis * km a km e i deg Ω deg ω deg Footnotes: * Distance from surface Author: Jeffrey Stuart

86 Project Bellerophon 117 Figure : Launch trajectory ground track, 5kg (Authors: Mike Walker, Alfred Lynam, Adam Waite) Figure is a ground track for the controlled portion of the launch. Ground tracks are important in the design of ground tracking stations and range safety concerns. The ground track is vital in the mission planning of the launch. Author: Jeffrey Stuart

87 Project Bellerophon Subsystem Details Propulsion The propellants we selected for the 5 kilogram payload launch vehicle were a hybrid first stage and a solid second and third stage. Our selection process involved the use of an optimization code which gave us the best results for a 5 kilogram payload launch vehicle. The code gave us a propulsion system described in the following section. The first stage of the launch vehicle uses a hybrid rocket motor, with hydrogen peroxide (H 2 O 2 ) as the oxidizer and hydroxyl terminated polybutadiene (HTPB) as the solid propellant. The H 2 O 2 tank is pressurized using gaseous nitrogen. The nozzle is a 12º conical nozzle with liquid injection thrust vector control (LITVC) attached. The LITVC system is composed of four valves that allow H2O2 to be injected into the nozzle at a 90º angle to the centerline of the nozzle. A schematic of the LITVC can be seen below in Figure Figure LITVC and Nozzle Configuration In Figure , the nozzle is shaded grey and all LITVC components are highlighted in orange. The pipes are run from the H 2 O 2 tank that is used for the hybrid motor, and then is distributed to each valve. The valves are connected to the controller which relays a signal for a Authors: Stephan Shurn, Ricky Hinton, Jerald A. Balta

88 Project Bellerophon 119 certain valve to open and allow pressurized H 2 O 2 to be injected into the main flow in the nozzle, which produces a side thrust. This side thrust allows for control of the launch vehicle during its ascent. The specifics of the propulsion system can be seen in Table Table kg Payload Stage 1 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 2,068,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass kg Thrust (vac) N Burn Time s Exit Area 1,198 m 2 Exit Pressure 2, Pa A conical nozzle was chosen because of the solid particles of propellant that will be coming out of the combustion chamber. The combustion process does not necessarily combust the fuel 100% and these particles can deteriorate a nozzle if it is let s say Bell shaped. Some of our early MAT codes had values based off of a 12 conical nozzle and that is one of the reasons we decided on this cone angle for the final design. Also having a smaller cone angle reduces the divergence loss at the exit of the nozzle. A picture of the nozzle can be seen below in Fig Authors: Stephan Shurn, Ricky Hinton, Jerald A. Balta

89 Project Bellerophon 120 Figure : Our 12 conical nozzle The second stage of the launch vehicle uses a solid rocket motor, with hydroxyl-terminated polybutadiene/ ammonium perchlorate/ aluminum (HTPB/AP/AL) as the propellant. The nozzle is a 12º conical nozzle with LITVC attached. The LITVC has the same configuration as the first stage, with the exception of the H 2 O 2. Since there is no H 2 O 2 already present due to the solid motor, a pressurized tank is added in a curved configuration sitting beneath the solid motor. The tank wraps around the nozzle and is pressurized with gaseous nitrogen so that the H 2 O 2 can flow into the lines for injection. The specifics of the propulsion system can be seen in Table Table kg Payload Stage 2 Propulsion Specifics Variable Value Units Vacuum Specific Impulse s Chamber Pressure 6,000,000 Pa Mass Flow Rate kg/s Propellant Mass kg Engine Mass kg Thrust (vac) N Burn Time s Exit Area m 2 Exit Pressure 11, Pa Authors: Stephan Shurn, Ricky Hinton, Jerald A. Balta