1. AAE 450 Spring 2008 Aerothermal 1 Brian Budzinski March 27, 2008 Aerothermal Group Contact Lifting Body Overview

2. Top Down View Fig. by Kyle Donohue AAE 450 Spring 2008 Aerothermal 2 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°). Wing Moment Coefficient versus AoA Fig. by Brian Budzinski

3. Shear on Launch Vehicle from Wing Fig. by Brian Budzinski Shear on Launch Vehicle from Fins 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. AAE 450 Spring 2008 Aerothermal 3

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

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

7. Side View Fig. by Kyle Donohue Launch vehicle with a pair of fins. Beneficial for: Stability Control Ground Launch Aircraft Launch Balloon Launch 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 Analysis Continued Lower Surface Eqns. A similar analysis can be done for a pair of fins. AAE 450 Spring 2008 Aerothermal 9

10. AAE 450 Spring 2008 Aerothermal 10 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.

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

12. 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.