1. AAE 450 Spring 20081 Brandon White 3/20/2008 Structures Group Contact Inert Mass Standard Deviation Justification Other Work

2. AAE 450 Spring 20082 Standard Deviation Justification “Happiness is the absence of striving for happiness.” – Chuang-Tzu  Value input into Monte Carlo: 2.255% –5 times the Vanguard 1 st Stage Std. Dev. –Accounts for small manufacturing tolerances. –High Tech Companies + Small Tolerances  High Costs  Final launch vehicles designed under the assumption of Space grade Aluminum –Cutting tolerances at.01”  Using Non-Space grade Aluminum shows opportunity for 200g and 1kg launch vehicles –Cutting tolerances at 0.125” Standard Deviations SB-HA-DA-DAMB-HA-DA-DALB-HA-DA-DA Monte Carlo2.255% Non-Space Grade2.28%2.32%8.94% Space-Grade3.13%2.88%4.42%

3. AAE 450 Spring 20083 Inertia Model “The person who writes for fools is always sure of a large audience.” – Arthur Shopenhauer  Geometry assumptions made due to unknown characteristics –Payload, Avionics in the 3 rd Stage all assumed to be a point mass located at the base of the Nose Cone –LITVC assumed to be a point mass at the base of the 1 st stage Nozzle –Avionics in the 1 st and 2 nd Stage assumed to be wall mounted to the inter-stage skirts Constant thickness of 10cm  Masses of each are minor in comparison to entire rocket, but this causes small inaccuracies in calculations SOLIDSOLID SOLIDSOLID S Skirt Pressurant Tank Oxidizer Tank Payload, Avionics Avionics LITVC

4. AAE 450 Spring 20084 Backup Slides – References  Krando Metal Products, http://www.krando.com/  Luminum, http://www.luminum.org/data/dtolaero.html “Art, like morality, consists in drawing the line somewhere.” –G.K. Chesterton

5. AAE 450 Spring 20085 Backup Slides – Thickness Tolerances for Aluminum “The beautiful thing about learning is nobody can take it away from you.” – B.B. King Thickness (meters) Tolerance +/- Greater ThanLess Than 0.000149860.0002540.0000254 0.0002540.00040640.0000381 0.00040640.0006350.0000381 0.0006350.00081280.0000381 0.00081280.00099060.0000381 0.00099060.00119380.0000508 0.00119380.00160020.0000508 0.00160020.00200660.0000508 0.00200660.00248920.0000635 0.00248920.00320040.0000889 0.00320040.00401320.0001016 0.00401320.00500380.0001524 0.00500380.00629920.0002286 0.00629920.0080010.0003048 0.0080010.01000760.0004318 0.01000760.0160020.0005842 0.0160020.02499360.0007874 0.02499360.0400050.0009906 0.0400050.05999480.001397 0.05999480.080010.001905 0.080010.09999980.00254 0.09999980.15999460.003302 Space Grade Non-Space Grade Credit: Molly Kane

6. AAE 450 Spring 20086 Inertia Matrix Math Model “If I’m not back in 5 minutes, wait longer.” – Ace Ventura  Calculates I xx, I yy, I zz at the center of mass of the launch vehicle  Assumes ALL products of inertia (ex. I xy ) equal to zero (vehicle is symmetric in radial directions)  Outputs values at different time steps. –First Stage: Full Propellant, Empty Propellant –Second Stage: Full Propellant, Empty Propellant –Third Stage: Full Propellant, Empty Propellant

7. AAE 450 Spring 20087 Evolution of Inertia Code PROPPROP PROPPROP PROPPROP SOLIDSOLID SOLIDSOLID S Skirt Pressurant Tank Oxidizer Tank Payload O O O F F F SOLIDSOLID SOLIDSOLID S Skirt Pressurant Tank Oxidizer Tank Payload, Avionics Avionics LITVC SOLIDSOLID SOLIDSOLID S “That’s it man, game over man, game over!” – Bill Paxton in Aliens