1. 1 Alex Woods March 20 Aerothermodynamics Group Force Model Walkthrough

2. Linear Perturbation  Forces are found by an integration of pressure distribution over the launch vehicle exterior  Integrations are done numerically within the code  Phi is the geometric angle w/respect to the freestream  S is a reference area, taken to be the area of the base of the launch vehicle  Validated by comparison to Vanguard results and other related geometries

3. Important Assumptions in Theory  Small changes in geometry  Small angle of attack ~ 0 – 14 degrees  Valid for subsonic or supersonic flow 0 < M < 0.88 1.12 < M < 5  Axial force neglects viscous effects

4. Stresses due to Aerodynamic Force  Shear Stress –Differential of Normal Force between stages  Axial Loading –A*q ∞ *S  Bending Moment  Picture by Jayme Zott and Alex Woods

5. Pictures

7. References  Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp. 303-312  Anderson, John D., Fundamentals of Aerodynamics, Mcgraw-Hill Higher Education, 2001  Professor Colicott, in reference to linearized theory applications

8. References Continued  Barrowman, James and Barrowman, Judith, "The Theoretical Prediction of the Center of Pressure" A NARAM 8, August 18, 1966. www.Apogeerockets.com www.Apogeerockets.com  Klawans, B. and Baughards, J. "The Vanguard Satellite Launching Vehicle - an engineering summary" Report No. 11022, April 1960  Morrisette, E. L., Romeo D. J., “Aerodynamic Characteristics of a Family of Multistage Vehicles at a Mach Number of 6.0”, NASA TN D-2853, June 1965

9. References Continued (2)  Professor Williams, concerning the use of pressure coefficients to determine aerodynamic forces  The entire Aerothermodynamics group for their invaluable help and support