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

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 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 Rectangular and polar coordinates All surfaces and 3D bodies on the same axes All surfaces and 3D bodies on the same axes Body design: Body design: – Cone – X 2 /A 2 + Y 2 /B 2 = Z 2 /C 2 – Circular Cylinder – X 2 /A 2 + Y 2 /B 2 = Z

Design Two Another rocket model was developed for comparison to the first model when analyzing air flow. Another rocket model was developed for comparison to the first model when analyzing air flow. Features: Features: – Less edgy – Smaller fins – More surface area Body design: Body design: – Elliptic Paraboloid – X 2 /A 2 + Y 2 /B 2 = Z/C

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

Fin Design Each fin is 90° from the others by shifting the place where it starts plotting along the x or y axes. 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. 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.