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Inertia Matrix Calculations for Rocket Stage Structures

This project, part of AAE 450 Spring 2008, focuses on calculating inertia matrices (Ixx, Iyy, Izz) for rocket stages based on propulsion data. It assumes all products of inertia are zero, reflecting symmetrical vehicle design. Outputs include stages’ dimensions and inert mass fractions, provided at different time steps for full and empty propellant conditions. Future work aims to enhance the model by incorporating the center of mass and internal structures. Acknowledgments to contributors, and references to essential materials are included.

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Inertia Matrix Calculations for Rocket Stage Structures

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  1. Brandon White1/31/2008Structures Group ContactInterface LoadsInertia Matrices / Structures Code AAE 450 Spring 2008

  2. Inertia Matrix Math Model • Currently calculates Ixx, Iyy,Izz at the tip of the nose cone. • 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 • Help provided by CJ Hiu (Thanks!) AAE 450 Spring 2008 Structures

  3. Tank Specification Model • Sizes the stages of the rocket based on inputs from propulsion data. • For each stage, Inputs: Tank Material, Tank Shape, Prop Type, Prop Volume, Mass, Chamber Pressure, Launch Vehicle Diameter. • Outputs: Tank Dimensions and Masses, Stage Dimensions and Masses, Inert Mass Fractions for each stage. Future Work • Transfer Inertia Matrix to the Center of Mass • Incorporate Internal Structure (Bulkheads, Mounts, Stringers, etc) to Tank Specification Model AAE 450 Spring 2008 Structures

  4. Backup Slides – References • Bedford, A., Fowler, W., and Liechti, K.M., Statics and Mechanics of Materials, Prentice Hall, Upper Saddle River, NJ. 2003 • Strauss, Chris. “Scaling_Program.xls”. 2008 • Thanks to Propulsion members J. Beasley, N. Wilcox, S. Bluestone, D. Lattibeaudiere for example inputs! AAE 450 Spring 2008 Structures

  5. Backup Slides – Example Output • Used Chris Strauss’ Scaling measurements for stage Diameter at 5kg Payload (Scale 2) • Tank Material was varied AAE 450 Spring 2008 “Structures Group = A OK!” – Time Magazine

  6. Backup Slides AAE 450 Spring 2008 “Structures: Built on Strong Foundations” – USA Today

  7. Backup Slides AAE 450 Spring 2008 “The way to get started is to quit talking and begin doing” – Walt Disney

  8. Backup Slides – Inertia Matrices for Example First Stage, Full First Stage, Empty Second Stage, Full Second Stage, Empty Third Stage, Full Third Stage, Empty - Aluminum 7075 Case AAE 450 Spring 2008 “You can take my word for it.” – Levar Burton

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