Brian Budzinski March 27, 2008 Aerothermal Group Contact Lifting Body Overview

1. Brian BudzinskiMarch 27, 2008Aerothermal Group ContactLifting Body Overview AAE 450 Spring 2008 Aerothermal

2. Wing Moment Coefficient versus AoA Fig. by Brian Budzinski Top Down View Fig. by Kyle Donohue Though an aircraft launch was not put into operation. A wing would be beneficial if it were. A wing creates an additional nose up pitching moment allowing the launch vehicle to pitch from an initial horizontal configuration (α=0°) into a final vertical configuration (α=90°). AAE 450 Spring 2008 Aerothermal 2

3. Shear on Launch Vehicle from Wing Fig. by Brian Budzinski Shear Coefficient on Launch Vehicle from Wing Fig. by Brian Budzinski The shear created through the addition of a wing or fins is assumed to be equal to the normal force caused by the corresponding part. Shear on Launch Vehicle from Fins Fig. by Brian Budzinski AAE 450 Spring 2008 Aerothermal 3

4. Wing Axial Force Coefficient versus AoA Fig. by Brian Budzinski Wing Normal Force Coefficient versus AoA Fig. by Brian Budzinski ASSUMPTIONS: Initial Horizontal Launch Configuration Final Vertical Configuration Newtonian Model Delta Wing AAE 450 Spring 2008 Aerothermal 4

5. Wing Lift Coefficient versus AoA Fig. by Brian Budzinski Wing Drag Coefficient versus AoA Fig. by Brian Budzinski ASSUMPTIONS: Initial Horizontal Launch Configuration Final Vertical Configuration Newtonian Model Delta Wing AAE 450 Spring 2008 Aerothermal 5

6. Once the lift and drag coefficients are determined, the lift versus drag curve can be created. Drag Coefficient versus Lift Coefficient Fig. by Brian Budzinski ASSUMPTIONS: Initial Horizontal Launch Configuration Final Vertical Configuration Newtonian Model Delta Wing AAE 450 Spring 2008 Aerothermal 6

7. Launch vehicle with a pair of fins. • Beneficial for: • Stability Control • Ground Launch • Aircraft Launch • Balloon Launch Side View Fig. by Kyle Donohue Fins were not implemented because D&C was able to successfully control the launch vehicle without them. AAE 450 Spring 2008 Aerothermal 7

8. Wing Analysis Divide the wing up into two sections: leading edge and lower surface. These two are chosen because they are the two portions exposed to the relative wind once given an angle of attack. AAE 450 Spring 2008 Aerothermal 8

9. Wing AnalysisContinued Lower Surface Eqns. A similar analysis can be done for a pair of fins. AAE 450 Spring 2008 Aerothermal 9

10. Assumptions: • Used Historical Values for large variety of similar shaped rockets and scaled the drag coefficient accordingly to determine CD at α=0. • Also attempted CFD to determine CD at α=0. • Then used CD at α=0 in order to generate plots of CD 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 10

11. -Used pressure coefficient to calculate the axial and normal force coefficients. -Used the axial and normal force coefficients to calculate the drag coefficient. AAE 450 Spring 2008 Aerothermal

12. References • Hankey, Wilbur L., Re-Entry Aerodynamics, AIAA, Washington D.C., 1988, pp. 70-73 • Rhode, M.N., Engelund, W.C., and Mendenhall, M.R., “Experimental Aerodynamic Characteristics of the Pegasus Air-Launched Booster and Comparisons with Predicted and Flight Results”, AIAA Paper 95-1830, June 1995. • 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. 303-312 • The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No. 11022, April 1960. AAE 450 Spring 2008 Aerothermal