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

Standard Deviation Justification Value input into Monte Carlo: 2.255% 5 times the Vanguard 1st 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-DA MB-HA-DA-DA LB-HA-DA-DA Monte Carlo 2.255% Non-Space Grade 2.28% 2.32% 8.94% Space-Grade 3.13% 2.88% 4.42% AAE 450 Spring 2008 “Happiness is the absence of striving for happiness.” – Chuang-Tzu

Inertia Model Geometry assumptions made due to unknown characteristics Payload, Avionics S Geometry assumptions made due to unknown characteristics Payload, Avionics in the 3rd 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 1st stage Nozzle Avionics in the 1st and 2nd 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 Avionics Skirt SOLID Avionics Skirt Pressurant Tank Oxidizer Tank SOLID LITVC AAE 450 Spring 2008 “The person who writes for fools is always sure of a large audience.” – Arthur Shopenhauer

Backup Slides – References Krando Metal Products, http://www.krando.com/ Luminum, http://www.luminum.org/data/dtolaero.html AAE 450 Spring 2008 “Art, like morality, consists in drawing the line somewhere.” –G.K. Chesterton

Backup Slides – Thickness Tolerances for Aluminum Thickness (meters)   Tolerance +/- Greater Than Less Than 0.00014986 0.000254 0.0000254 0.0004064 0.0000381 0.000635 0.0008128 0.0009906 0.0011938 0.0000508 0.0016002 0.0020066 0.0024892 0.0000635 0.0032004 0.0000889 0.0040132 0.0001016 0.0050038 0.0001524 0.0062992 0.0002286 0.008001 0.0003048 0.0100076 0.0004318 0.016002 0.0005842 0.0249936 0.0007874 0.040005 0.0599948 0.001397 0.08001 0.001905 0.0999998 0.00254 0.1599946 0.003302 Space Grade Non-Space Grade Credit: Molly Kane AAE 450 Spring 2008 “The beautiful thing about learning is nobody can take it away from you.” – B.B. King

Inertia Matrix Math Model Calculates Ixx, Iyy, Izz at the center of mass of the launch vehicle Assumes ALL products of inertia (ex. Ixy) 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 AAE 450 Spring 2008 “If I’m not back in 5 minutes, wait longer.” – Ace Ventura

Evolution of Inertia Code Payload, Avionics Payload S Avionics Skirt S Skirt O S PROP SOLID F SOLID SOLID PROP O Avionics F Skirt Skirt Pressurant Tank Pressurant Tank PROP Oxidizer Tank O Oxidizer Tank SOLID SOLID F SOLID LITVC AAE 450 Spring 2008 “That’s it man, game over man, game over!” – Bill Paxton in Aliens