1. AAE 450 Spring 2008 Stephanie Morris 2/21/08 Propulsion Standard Deviations

2. AAE 450 Spring 2008 Propulsion Propulsion Standard Deviations Average Total Propellant Mass (lb) (Vanguard) 20,057 Standard Deviation (Vanguard) 69 % Deviation (Vanguard) 0.3440 Estimated Propellant Mass (kg) 4,622 Estimated Standard Deviation 15.90 Using the standard deviation values from the Vanguard report, the standard deviations for the propellant mass of our launch vehicle were estimated. Assumptions: Launch vehicle of LG-CA-DA-DT. Current launch vehicle output values for propellant mass and mass flow rates are accurate. Percent standard deviation can be used to compute standard deviations for our LV.

3. AAE 450 Spring 2008 Propulsion Propulsion Standard Deviations First StageSecond Stage Average Mass Flow Rate (lb/sec) (Vanguard) 110.727.4 Standard Deviation (Vanguard) 0.5450.4 % Deviation (Vanguard) 0.49231.460 Estimated Mass Flow Rate (kg/sec) 17.971.814 Estimated Standard Deviation 0.08850.0265 Future Work: Check standard deviation against other launch vehicles.

4. AAE 450 Spring 2008 References Burkhardt, H., Herbertz, A., Sippel, M., Klevanski, J. “Solid Propellant Hypersonic X-Vehicle Options as RLV Technology Stepping Stones”. Space Launcher Systems Analysis. 2002. Isakowitz, Steven J., Hopkins, Joshua B., Hopkins, Joshua P Jr. International Reference Guide to Space Launch Systems. Fourth Edition. AIAA, Reston, VA 2004 Martin Company, The Vanguard Satellite Launching Vehicle, Engineering Report No.11022. April 1960, pp. 26, 208 Propulsion

5. Historical Data for Comparison AAE 450 Spring 2008 Engine NamePropellant Thrust (avg) kN Dry Mass (kg) Mass Flow rate (kg/s) Chamber Pressure (psi) HM7BLOX/LH264.80155.0014.40 LE-5LOX/LH2100.00255.0023.10 LE-5ALOX/LH2121.50245.0026.90 LE-5BLOX/LH2137.00269.00 522.14 RD-0126ALOX/LH298.00340.00 1711.45 RD-0146LOX/LH298.10260.00 1145.80 RL10A-3-3ALOX/LH273.00140.5016.80 RL10A-4LOX/LH288.20168.00 RL-10A-5KALOX/LH2100.49145.00 591.90 RL10B-2LOX/LH2110.00301.00 RL-10CLOX/LH2155.00317.00 1479.38 RL-10C-XLOX/LH2110.80317.00 1479.38 VinciLOX/LH2180.00480.0033.80 RS-58SLOX/KEROSENE86.30230.00 1151.60 RD-0242-HCLOX/KEROSENE125.00120.00 2845.64 RD-169LOX/KEROSENE167.00215.00 2132.05 RD-185LOX/KEROSENE179.00415.00 2132.05 RD-0245-HCLOX/KEROSENE214.00290.00 2059.54 Star 63DHTPB84.74249.30 607.00 X-259HTPB93.10300.00 Star 63FHTPB104.62327.20 680.00 SRM-1HTPB186.001134.00 841.22 S40HTPB202.00929.0071.45829.62 Zefiro 9HTPB230.00690.0076.90710.68

6. Section of Final Report AAE 450 Spring 2008 In order to compute the accuracy using the “Monte Carlo” method, the propulsion standard deviations of mass flow rate and propellant mass must be calculated. Using values from the Vanguard report for the standard deviation and average value, the percent deviation was computed using Equation (1). % Deviation = Standard Deviation / Average ValueEq.(1) Once the percent deviation was obtained, the value for propellant mass and mass flow rate, at each stage, was used to calculate the standard deviation for our launch vehicle. For example, Standard Deviation = % Deviation * Propellant MassEq.(2) Using the output values of propellant mass and mass flow rates, the standard deviation was calculated. For total propellant mass the standard deviation is 15.9. The standard deviation for mass flow rate of the first stage is 0.0885 and the second stage is 0.0265.