AAE 450 Spring 2008 Propulsion Back-Up Slides Propulsion

AAE 450 Spring 2008 Engine Performance Characteristics I sp,vac (s) I sp (s) Chamber Pressure (Mpa) O/F Ratio C* (m/s) Exit Mach #Ae/At Stage Stages 2, Propulsion

AAE 450 Spring 2008 Propellant and Pressurant Cost  Propellant –Stage 1 - Hydrogen Peroxide and HTPB –Stage 2,3 - AP/HTPB/Al  Pressurant –Nitrogen –12 MPa –1 st Stage Only Propulsion VehicleStage Propellant Mass (kg) Propellant Cost ($) Pressurant Mass (kg) Pressurant Cost ($) 200 g $14, $ $2, $187-- Total2065.9$17, $ kg $9, $ $1, $226-- Total1330.0$11, $ kg $41, $ $5, $192-- Total5169.8$46, $83.15

Mixture Ratio Optimization O/F Hybrid ~ 6Hybrid – H2O2/HTPB

Pressure vs. Pump

Top Twelve Propellants

Change in Performance  Min Alt. for no separation – 21,900 m  Separation Ae/At = 3.25  Isp,v =  Isp, sl =  % Diff Isp From Launch Alt = 16 % Thrust,vac (N)Thrust,sl (N)% Diff Thrust 200 g % 1 kg % 5 kg %

Prop Mass and Fraction Per Stage Mass Prop (kg)Mass Stage (kg)Prop Mass Fraction Per Stage 200 g Stage % Stage % Stage % 1 kg Stage % Stage % Stage % 5 kg Stage % Stage % Stage %

Payload Mass and Fractions Mass Payload Third Stage Mass (kg) Payload Mass Fraction Stage 3 (kg)Total Mass (kg) Payload Mass Fraction Total % % % % % %

Stage Mass and Allocation Mass Stage (kg)Mass Allocation Per Stage 200 g Stage % Stage % Stage % 1 kg Stage % Stage % Stage % 5 kg Stage % Stage % Stage %

Percent Delta V Breakdown StageDelta V Percentage 200 g Stage % Stage % Stage % 1 kg Stage % Stage % Stage % 5 kg Stage % Stage % Stage %

12 Engine Sizing  The amount of propellant required for each rocket/stage was determined in Model Analysis  Inert mass fraction, f inert, was optimized between the structures and propulsion groups for final design

13 Engine Cost  Cost of Engines calculated from equations based on mass flow, thrust, and dry weight  Cost equations are extrapolated from historical values Payload1 st Stage Engine Cost 2 nd Stage Engine Cost 3 rd Stage Engine Cost Total Engine Cost 200g$679,720$263,690$79,930$1,023,340 1kg$634,090$209,930$86,860$930,880 5kg$1,138,700$339,700$80,900$1,559,300

14 Historical Failure Probability  U.S. Solid Rocket Systems (Failures/Attempts) –6 / 412 (1.4%) Failures between –19 / 3382 (0.56%) Failures between  Solid Propulsion Failure Rates (Failures/Attempts) –Upper Stage /10000 –Monolithic /10000 –Segmented /10000 –Total /10000 AAE 450 Spring 2008 Propulsion – Propellants

Engine Performance Characteristics AAE 450 Spring g Launch Vehicle Stage 1Stage 2Stage 3 Vacuum Thrust [N]34,0458, Mass Flow [kg/s] Burn time [s] Propellant Mass [kg]1, Exit Area [m^2] Exit Pressure [Pa]2,82111,454 Nozzle Length [m] Engine mass [kg] Pressure of ox, fuel tanks [MPa]

Engine Performance Characteristics AAE 450 Spring kg Launch Vehicle Stage 1Stage 2Stage 3 Vacuum Thrust [N]21,4366, Mass Flow [kg/s] Burn time [s] Propellant Mass [kg] Exit Area [m^2] Exit Pressure [Pa]2,82111,454 Nozzle Length [m] Engine mass [kg] Pressure of ox, fuel tanks [MPa]

Engine Performance Characteristics AAE 450 Spring kg Launch Vehicle Stage 1Stage 2Stage 3 Vacuum Thrust [N]75,07315, Mass Flow [kg/s] Burn time [s] Propellant Mass [kg]4,1231, Exit Area [m^2] Exit Pressure [Pa]2,82111,454 Nozzle Length [m] Engine mass [kg] Pressure of ox, fuel tanks [MPa]

AAE 450 Spring 2008 Propulsion Hybrid and Solid Standard Deviations Hybrid Propellant Solid PropellantLiquid PropellantHybrid Propellant Mass of Propellant 0.12 %0.734 %0.854 % Mass flow rate1.0 % % % For hybrid propellants, we cannot find historical standard deviations. The two percent deviations for liquid and solid propellant are added together to calculate a hybrid propellant percent standard deviation. Percent Deviations for Each Propellant Type

AAE 450 Spring 2008 LITVC  1 st and 2 nd stage control  4 valves per stage for perpendicular to centerline injection of H 2 O 2  1 st stage tap-off of main H 2 O 2 tank  2 nd stage bring own H 2 O 2 pressurized tank  Considered main part of engine for weight/cost due to low complexity  Costs include: –4 valves per $100/valve –Extra propellant –Extra tank on 2 nd stage Propulsion

AAE 450 Spring 2008 LITVC Calculations  Input –Thrust (vac) –Mass Flow rate –Stage Burn Time  Calculations Propulsion Image courtesy E. Glenn Case IV 1

AAE 450 Spring 2008 Ideal Mass Ratios Propulsion Team Stage #Bellerophon (1 kg) Saturn VPegasus

Mass Ratio Comparison (1 kg case) Stage #IdealActual

AAE 450 Spring 2008 References  Heister, Stephen D.  Humble, R. W., Henry, G. N., Larson, W. J., Space Propulsion Analysis and Design, McGraw-Hill, New York, NY,  Javorsek, D., and Longuski, J.M., “Velocity Pointing Errors Associated with Spinning Thrusting Spacecraft,” Journal of Spacecraft and Rockets, Vol. 37, No. 3, 2000, pp  Klaurans, B. “The Vanguard Satellite Launching Vehicle,” The Martin Company. No , April  Knauber, R.N., “Thrust Misalignments of Fixed-Nozzle Solid Rocket Motors,” Journal of Spacecraft and Rockets, Vol. 33, No. 6, 1996, pp  Sutton, George P., Biblarz, Oscar “Solid Propellants,” Rocket Propulsion Elements, 7 th ed., Wiley, New York,  Ventura, M., “The Lowest Cost Rocket Propulsion System,” General Kinetics Inc, Huntington Beach, CA, Jul  Tsohas, John. Propulsion

AAE 450 Spring 2008 Balloon Design Helium – Priced at $4.87 per cubic meter of gas Balloon – Price quote from Aerostar International Gondola- Constant Price of $13,200

Balloon Model  Free Body Diagram  Two forces acting on Spherical Balloon –Buoyancy Force Defined by difference between masses of lifting gas and air multiplied by gravitational constant –Weight Buoyancy Weight

Derivation of Balloon Dimensions  Lifting Coefficient –Ρ g is density of lifting gas –Ρ a is density of air  Boyle’s and Gay Lussac’s laws –Rho is density –P is pressure –T is Temperature

Derivation of Balloon Dimensions Continued  Combine equations to determine lifting coefficient for different heights  Take into account 95% gas purity and standard excess of 15% lifting gas  Final Equation for Volume of Gas in relation to Mass –V is volume of lifting gas –M total is total mass

Balloon Cost AAE 450 Spring 2008 Cost Trend Equation  Y = X X  Y = Cost  X = Balloon Payload

Gondola Costs Structures Cost of $1,200 Material Welding Riveting Avionics Cost of $12,000 One Battery Sensors  Total Gondola Cost of $13,200 Provided by Sarah Shoemaker, Structures Group, and Avionics Group

AAE 450 Spring 2008 Propulsion Lift Weight D Vertical Determination of rise time Assumptions Constant sphere Constant C D = 0.2 Barometric formula Kinematic viscosity variation with temperature Constant acceleration over time steps of 1 second D Horizontal

Thanks to Jerald Balta for modifying the balloon code to output this.

Ground Support and Handling Cost Modifier  Handling – Personnel required for handling of fuels, toxic materials, etc  Ground Support – Based on estimation of salaries of necessary personnel –Assumed $100/hour salary –Six engineers and one project manager

Cost Modifier

References  Defense Energy Support Center, “MISSILE FUELS STANDARD PRICES EFFECTIVE 1 OCT 2007,” Aerospace Energy Reference, November 2007  Larson, W.J., Wertz, J.R., "Space Cost Modeling," Space Mission Analysis and Design, 2nd ed., Microcosm, Inc., California and Kluwer Academic Publishers, London, 1992, pp  Smith, Mike, Phone Conversation, Aerostar International, February 15, 2008  Tangren, C.D., "Air Calculating Payload for a Tethered Balloon System," Forest Service Research Note SE-298, U.S. Department of Agriculture - Southeastern Forest Experiment Station, Asheville, North Carolina, August 1980.

Nozzle (specs and CAD)  Conical Nozzle –12° Conical Nozzle –Conical because of solid and hybrid propellants. –All stages have same nozzle  Sizing –Nozzle Dimensions based off of the exit area from MAT output –ε = 60; Throat Area and Throat Diameter are determined. CaseD throat (m) D exit (m) A throat (m^2) A exit (m^2) D stage (m) 5 kg Stage Stage Stage kg Stage Stage Stage g Stage Stage Stage

Nozzle Dimensions per stage (Metric & English units)

Test Facilities Purdue (Zucrow High Pressure Laboratories)  Propellants/ Oxidizers currently tested: H 2 O 2, Liquid Hydrocarbon, LOX  For Hybrid test we need H 2 O 2, and (excluding 5 kg Stage1) all other engines can be tested at Purdue.  Table below shows Zucrow’s HPL capabilities.  Kelly Space and Technology  Up to 20,000 lbf (88,960 N) thrust stand capabilities.  Propellant tanks and data acquisition systems already at test site.  Located in San Bernardino, CA.  Can test our 5 kg: stage 1 engine at 75,073 Newtons of thrust. Maximum Capability ValueUnits Thrust44,480N Chamber Pressure4.137MPa Mass Flow Rate6.803kg/s

References  1 Scott Meyer, private meeting at Zucrow Test Laboratories. February 8 th, Test facility overview and private tour of the large rocket test stand.  2 Kelly Space and Technology. Jet and Rocket Engine Test Site (JRETS) URL: [last updated Jan. 31 st 2008].  3 MAT Output file from AAE 450 course website. 5kg, 1kg, and 200 g cases _5kg/v125/5kg_MAT_out_v125.txt _5kg/v125/5kg_MAT_out_v125.txt AAE 450 Spring 2008