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Rocket Modeling Using 3-D Graphing and Air Flow Analysis

This project investigates rocket design through advanced mathematical modeling using Maple software. We created two distinct rocket models to analyze their design and airflow characteristics. The first model employs a conical body shape, while the second model features an elliptic paraboloid to optimize aerodynamic efficiency. Key computational elements include converting between Cartesian and polar coordinates for precise plotting, ensuring effective fin design, and analyzing airflow dynamics. Ultimately, this work aims to enhance rocket performance through innovative design techniques grounded in mathematical principles.

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Rocket Modeling Using 3-D Graphing and Air Flow Analysis

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  1. Footnote 18 MAT267 Professor Brewer April 28, 2008 Project by Vishal Doshi and Erin Eppard Rocket Modeling Using 3-D Graphing and Air Flow Analysis

  2. Design One • Using Maple, a professional math software application, a three dimensional plotting command, was used to define the surfaces and 3D bodies in our rocket • Rectangular and polar coordinates • All surfaces and 3D bodies on the same axes • Body design: • Cone • X2/A2 + Y2/B2 = Z2/C2 • Circular Cylinder • X2/A2 + Y2/B2 = Z

  3. Design Two • Another rocket model was developed for comparison to the first model when analyzing air flow. • Features: • Less edgy • Smaller fins • More surface area • Body design: • Elliptic Paraboloid • X2/A2 + Y2/B2 = Z/C

  4. Designing the Rockets • Calculations: • Intercepts • Desired curvature • Conversion between Cartesian and polar coordinates for most efficient plotting • Considerations: • Aerodynamics • Proportionality • Limited knowledge of 3D surface equations

  5. Fin Design • Each fin is 90° from the others by shifting the place where it starts plotting along the x or y axes. • In order for it to be a plane on the y and z axes, the x axis must be zero, whereas on the x and z axes, the y axis must be zero.

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