1. AAE 450 Spring 2008 Propulsion Back-Up Slides Propulsion

2. 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 1352.3337.62.16.01752.04.460 Stages 2,3309.3292.16.01.01480.04.160 Propulsion

3. 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 11462.0$14,65059.0$29.50 2566.6$2,833-- 337.3$187-- Total2065.9$17,67059.0$29.50 1 kg 1947.9$9,50038.2$19.10 2336.9$1,685-- 345.1$226-- Total1330.0$11,41038.2$19.10 5 kg 14122.2$41,320166.3$83.15 21009.2$5,046-- 338.4$192-- Total5169.8$46,560166.3$83.15

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

5. Pressure vs. Pump

6. Top Twelve Propellants

7. Change in Performance  Min Alt. for no separation – 21,900 m  Separation Ae/At = 3.25  Isp,v = 283.1  Isp, sl = 245.3  % Diff Isp From Launch Alt = 16 % Thrust,vac (N)Thrust,sl (N)% Diff Thrust 200 g340502610023.36% 1 kg 21440 1644023.33% 5 kg 75070 5767023.19%

8. Prop Mass and Fraction Per Stage Mass Prop (kg)Mass Stage (kg)Prop Mass Fraction Per Stage 200 g Stage 11462181180.71% Stage 256772078.69% Stage 3375271.57% 1 kg Stage 1948104590.71% Stage 233736891.66% Stage 3455188.50% 5 kg Stage 14123453091.01% Stage 21009110091.75% Stage 3384388.40%

9. Payload Mass and Fractions Mass Payload Third Stage Mass (kg) Payload Mass Fraction Stage 3 (kg)Total Mass (kg) Payload Mass Fraction Total 0.252.060.38%25840.01% 150.951.96%14630.07% 543.4111.52%56740.09%

10. Stage Mass and Allocation Mass Stage (kg)Mass Allocation Per Stage 200 g Stage 1181170.11% Stage 272027.87% Stage 3522.02% 1 kg Stage 1104571.40% Stage 236825.12% Stage 3513.48% 5 kg Stage 1453079.85% Stage 2110019.39% Stage 3430.77%

11. Percent Delta V Breakdown StageDelta V Percentage 200 g Stage 135.00% Stage 235.00% Stage 330.00% 1 kg Stage 135.00% Stage 230.00% Stage 335.00% 5 kg Stage 140.00% Stage 235.00% Stage 325.00%

12. 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. 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. 14 Historical Failure Probability  U.S. Solid Rocket Systems (Failures/Attempts) –6 / 412 (1.4%) Failures between 1980-2004 1 –19 / 3382 (0.56%) Failures between 1964-1998 2  Solid Propulsion Failure Rates (Failures/Attempts) –Upper Stage 0.0161 161/10000 –Monolithic 0.0025 25/10000 –Segmented 0.0077 77/10000 –Total 0.005656/10000 AAE 450 Spring 2008 Propulsion – Propellants

15. Engine Performance Characteristics AAE 450 Spring 2008 200g Launch Vehicle Stage 1Stage 2Stage 3 Vacuum Thrust [N]34,0458,783625.0 Mass Flow [kg/s]10.692.7380.1942 Burn time [s]136.8207.7191.9 Propellant Mass [kg]1,462566.637.26 Exit Area [m^2]0.54300.04000.0030 Exit Pressure [Pa]2,82111,454 Nozzle Length [m]1.7040.46450.1239 Engine mass [kg]96.9451.538.40 Pressure of ox, fuel tanks [MPa]2.076.00

16. Engine Performance Characteristics AAE 450 Spring 2008 1 kg Launch Vehicle Stage 1Stage 2Stage 3 Vacuum Thrust [N]21,4366,052743.4 Mass Flow [kg/s]6.7301.8800.2310 Burn time [s]140.8179.2195.3 Propellant Mass [kg]947.9336.945.09 Exit Area [m^2]0.34220.02780.00340 Exit Pressure [Pa]2,82111,454 Nozzle Length [m]1.3520.38560.1352 Engine mass [kg]72.6236.449.534 Pressure of ox, fuel tanks [MPa]2.076.00

17. Engine Performance Characteristics AAE 450 Spring 2008 5 kg Launch Vehicle Stage 1Stage 2Stage 3 Vacuum Thrust [N]75,07315,257692.4 Mass Flow [kg/s]23.574.740.22 Burn time [s]174.9213.0178.4 Propellant Mass [kg]4,1231,00938.37 Exit Area [m^2]1.1980.07000.0030 Exit Pressure [Pa]2,82111,454 Nozzle Length [m]2.5300.61220.1304 Engine mass [kg]193.575.728.560 Pressure of ox, fuel tanks [MPa]2.076.00

18. 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 %0.4923 %1.4923 % 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

19. 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 stage @ $100/valve –Extra propellant –Extra tank on 2 nd stage Propulsion

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

21. AAE 450 Spring 2008 Ideal Mass Ratios Propulsion Team Stage #Bellerophon (1 kg) Saturn VPegasus 13.4673.4902.817 22.7492.6362.685 31.9451.8052.171 4-- 1.186

22. Mass Ratio Comparison (1 kg case) Stage #IdealActual 13.4672.343 22.7493.155 31.9453.216

23. 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, 1995.  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. 359-360.  Klaurans, B. “The Vanguard Satellite Launching Vehicle,” The Martin Company. No. 11022, April 1964.  Knauber, R.N., “Thrust Misalignments of Fixed-Nozzle Solid Rocket Motors,” Journal of Spacecraft and Rockets, Vol. 33, No. 6, 1996, pp. 794-799.  Sutton, George P., Biblarz, Oscar “Solid Propellants,” Rocket Propulsion Elements, 7 th ed., Wiley, New York, 2001.  Ventura, M., “The Lowest Cost Rocket Propulsion System,” General Kinetics Inc, Huntington Beach, CA, Jul. 2006.  Tsohas, John. Propulsion

24. 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

25. 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

26. 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

27. 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

28. Balloon Cost AAE 450 Spring 2008 Cost Trend Equation  Y = -0.0011X 2 + 30.62X + 3111.1  Y = Cost  X = Balloon Payload

29. 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

30. 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

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

34. 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

35. Cost Modifier

36. 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. 715-731.  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.

37. 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 10.1591.2350.02001.1981.839 Stage 20.00390.2990.00170.0700.817 Stage 30.0080.06180.000050.0030.275 1 kg Stage 10.0850.6600.00570.3421.126 Stage 20.0240.1890.000470.0280.567 Stage 30.0080.0620.000050.0030.290 200 g Stage 10.1070.8310.009050.5431.302 Stage 20.0290.2260.000670.040.674 Stage 30.0080.0620.000050.0030.272

38. Nozzle Dimensions per stage (Metric & English units)

39. 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

40. References  1 Scott Meyer, private meeting at Zucrow Test Laboratories. February 8 th, 2008. 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: http://www.kellyspace.com/ [last updated Jan. 31 st 2008].  3 MAT Output file from AAE 450 course website. 5kg, 1kg, and 200 g cases https://engineering.purdue.edu/AAE/Academics/Courses/aae450/2008/spring/large/3 _5kg/v125/5kg_MAT_out_v125.txt https://engineering.purdue.edu/AAE/Academics/Courses/aae450/2008/spring/large/3 _5kg/v125/5kg_MAT_out_v125.txt AAE 450 Spring 2008