AAE 450 Spring 2008 Aerothermal 1 Brian Budzinski March 6, 2008 Aerothermal Group Contact History of the Drag Model Assistance from: Jayme Zott & Alex Woods

AAE 450 Spring 2008 Aerothermal 2 Assumptions: -Used Historical Values for large variety of similar shaped rockets and scaled the drag coefficient accordingly to determine C D at α=0. -Also attempted CFD to determine C D at α=0. -Then used C D at α=0 in order to generate plots of C D versus AoA. -”Normal” Geometry indicates all upper stages are smaller in diameter than their predeceasing lower stage and only a total of 1 to 2 shoulders.

AAE 450 Spring 2008 Aerothermal 3 Assumptions: Future Work: Write Report Compose Final Report Slides -Used pressure coefficient to calculate the axial and normal force coefficients. -Used the axial and normal force coefficients to calculate the drag coefficient.

Linear Perturbation Theory:  Linearized Subsonic Theory Cp=2θ/√(1-M 2 )  Linearized Supersonic Theory Cp=2θ/√(M 2- 1) Where θ is the geometric angle and M is the mach number  Axial Force Coefficient C A =(1/S) ∫(Cp U +Cp L )∙2dy ∙π ∙diameter  Drag Coefficient C D =N ∙ sin(α) + A ∙cos(α) Where S is the reference area (area of the base of the rocket), Cp U is the upper pressure coefficient, Cp L is the lower pressure coefficient, N is the normal force, A is the axial force, and α is the angle of attack. AAE 450 Spring 2008 Aerothermal 4

Remarks:  Model is not completely accurate for transonic flow; however, most aerodynamic theories fall apart in the transonic region.  Model is not accurate for hypersonic flow. -For mach 6.0, C D should be 0.2 however, we were getting This is justified though, since the rocket is traveling at approximately mach 4.5 when it exits the atmosphere, from the balloon launch (which is still supersonic flow). AAE 450 Spring 2008 Aerothermal 5

AAE 450 Spring 2008 Aerothermal 6 References:  Alex Woods and Jayme Zott  Anderson, John D., Fundamentals of Aerodynamics, Mcgraw-Hill Higher Education, 2001  Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp  The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No , April 1960.

AAE 450 Spring 2008 Aerothermal 7 Work Outline Aerothermal Group Contact  Interface between groups  Interface within group CFD  CATIA Model  Gambit Mesh  FLUENT Lifting Bodies  Wing -C D, C L, C M, Shear  Fins -C D, C L, C M, Shear Monte Carlo  Compiled Spreadsheet for drag variance Final Slides/Report  Outlined the Drag Model  Looked into Risk/Cost Analysis