New capability has been added to the NSWC aeroprediction code to allow aerodynamics to be predicted for Mach numbers up to 20 for configurations with flares. This new capability includes extending the static aerodynamic predictions for Mach numbers less than 1.2, improving the body alone pitch damping for Mach numbers above 2.0, and developing a new capability for pitch damping of flared configurations at Mach numbers up to 20.This new capability for flared configurations was validated for several different configurations in the Mach number range of 2 to 8.8. In general, pitch damping predictions of the improved capability was within 20 percent of either experimental data or computational fluid dynamics calculations. This accuracy level is believed to be quite adequate for dynamic derivatives in the preliminary design stage. These new additions to the aeroprediction code will be transitioned to users as part of the 2002 version of the code (AP02).

The capability of accurately estimating pitch damping values for missile-like geometries over a range of Mach numbers and at high angles of attack using state-of-the-art CFD techniques has been investigated. Toward this effort three geometries were examined: the Army-Navy Finner model, the extended Army-Navy Finner model, and the M823 research store. Pitch damping values are predicted using forced oscillation calculations performed with the RavenCFD Navier-Stokes flow solver. Additionally, pitch decay calculations and aerodynamic build-up methods are also employed using the RavenCFD solver. These methods are compared to both experimental results and AP09, a fast-running engineering tool. Pitch damping variations due to geometric changes, Mach number changes, and angle of attack changes are explored with each method. Overall, each CFD method exhibits an outstanding agreement with experiment and range data at the lower angles of attack. Both pitch decay and forced oscillation approaches provide good agreement for low-to-moderate angles. At angles of attack greater than 30 degrees, the forced oscillation approach provides the best agreement. Pitch damping variations at angles higher than 60-70 degrees for the Army-Navy Finner have been shown to be a peripheral effect of the extreme unsteadiness of the wake flow at these conditions. NomenclatureA = amplitude of oscillation k = reduced frequency c = chord C m = pitching moment coefficient ̇ = pitch damping sum = normal force coefficient = normal force curve slope d ref = reference length (typically missile diameter) FOA = Forced Oscillation Approach yy I = moment of inertia about the pitch axis k = reduced frequency, M = Mach number ncyc = number of points per cycle PD = Pitch Decay Approach 2 q = dynamic pressure, = reference area tp = time for given peak (used in pitch decay) t = time U ∞ = freestream velocity w = aerodynamic load = x-location of the i th missile panel (used in build-up approaches) xcg = x-location of the center of gravity xcp = x-location of the model center of pressure α = angle of attack α m = mean angle of attack α o = angle of attack amplitude α p = peak pitch angle (used in pitch decay) t = time step = width of the i th missile panel (used in build-up approaches)  = ratio of specific heats  = density  = angular frequency

Future missile designs must expand the current flight envelope to continue to be effective against next generation aircraft. As such, design tools must be improved to increase the accuracy of aerodynamic predictions over a larger range of flight conditions. Computational fluid dynamics (CFD) results of the Sparrow missile configuration over a wide range of flight attitudes and Mach numbers are presented herein to assist in the development of design tools, such as fast running semi-empirical engineering codes. In addition, the CFD results are used to investigate complex physical phenomena, such as wing-wing, wing-body, and wing-tailfin interaction to assist in developing modeling procedures. It was found that these interactions play a significant role in the nonlinearity of rolling moment at higher angles of attack. Nomenclature AOA= angle of attack C l = rolling moment coefficientMember AIAA. † Aerospace Engineer, Member AIAA. ‡ President, Aeroprediction, Inc., Associate Fellow AIAA. AIAA SciTech M = Mach number P tot = total pressure α = angle of attack [degrees] δ = wing/tail deflection [degrees] φ = roll angle [degrees]

Results from computational fluid dynamics (CFD) predictions of roll damping on three elementary missile configurations are presented in this work. RavenCFD, a threedimensional unstructured-grid Navier-Stokes solver, is used in conjunction with a rigid body motion (RBM) capability and an embedded six-degree-of-freedom (6-DOF) solver to simulate both prescribed rolls and free-to-roll configurations.Several different methodologies are applied to both prescribed-roll and free-to-roll CFD calculations to obtain estimates of roll damping coefficient across a broad range of Mach numbers. In general, the computational results agree well with experimental roll-damping measurements across the range of Mach numbers and angles of attack considered. Nomenclatureα = Angle of attack ϕ = Roll angle C lp = Roll damping coefficient C l = Rolling moment coefficient d = Configuration base diameter I xx = Moment of inertia about roll axis M ∞ = Freestream Mach number U ∞ = Freestream velocity T ∞ = Freestream temperature p = Roll rate pd/2U ∞ = Nondimensional roll rate p ∞ = Freestream pressure q ∞ = Freestream dynamic pressure S = Configuration reference area

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