Alex Woods January 24th Aerodynamics Determination and Influences of Center of Pressure AAE 450 Spring 2008

Analytic Cases Subsonic – Vanguard geometry Transonic Supersonic Lateral Area – 55.99% lfn Barrowman – 25.73% lfn Transonic Detailed Analysis Forthcoming Vanguard Case: ~50% lfn Supersonic Holt Ashley ~ .3654% lfn lfn = Body length from nose Coefficients pulled from Holt Ashley, applied to Vanguard geometrical case AAE 450 Spring 2008 Group Name (i.e.Trajectory Optimization)

Influences of CP Considerations Future Work Geometry Angle of Attack Primarily influenced by nose, shoulders, boat-tails, and fins Angle of Attack Most rockets travel at < 6% angle of attack Influenced by horizontal wind patterns Mach Number Moves aft while M ≤ 1 Moves back for M > 1 Becomes Mach independent for hypersonic flow Most Classic Rocket shapes are statically unstable for the open loop case Maintaining a CP behind the CG will be difficult without the use of fins Blunt nose cones increase drag but decrease normal loads and pitching moment Future Work Transonic Case Analysis CFD Analysis of Pressure Distribution Linearized Flow and Newtonian for Analysis of Super / Hypersonic Cases AAE 450 Spring 2008 Group Name (i.e.Trajectory Optimization)

Backup Slides References (1)Barrowman, James and Barrowman, Judith, "The Theoretical Prediction of the Center of Pressure" A NARAM 8, August 18, 1966. www.Apogeerockets.com (2) Wade, Mark; "Vanguard" Stage Data http://astronautix.com/lvs/vanguard.htm (3) Klawans, B. and Baughards, J. "The Vanguard Satellite Launching Vehicle - an engineering summary" Report No. 11022, April 1960 AAE 450 Spring 2008 Group Name (i.e.Trajectory Optimization)

References Cont. (4) Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp. 303-312 (5) 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 Thanks to the Aerothermodynamics team for advice and direction AAE 450 Spring 2008

Assumptions Subsonic Cases Lateral Area Barrowman (lifted from report) 1. Ninety Degree AOA 2. Uniform aerodynamic force across surfaces incident to flow 3. No significant lifting surfaces (wings) Barrowman (lifted from report) All flow is potential flow Point of the nose is sharp Fins are thin plates with no cant The angle of attack is very near zero Flow is steady state and subsonic The rocket is a rigid body The rocket is axially symettric AAE 450 Spring 2008

Assumptions (Cont.) Hypersonic (Ashley case) Flow is mach number independent Pitch axis is located at the center of lateral area Geometry of the Vanguard is reasonably close to that used in the Morrisette and Romeo wind tunnel tests AAE 450 Spring 2008