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Aerodynamic damping derivatives measured as function of instantaneous angular displacement and relationship to damping derivatives measured as function of oscillation amplitude
Experimental studies to determine the 140-deg spherically-blunted cone configuration single degree-of-freedom damping derivative included model sting interference effects at M = 1.76 to 3.0. Minimal sting influences are noted with sting/model diameter ratios of 0.183 and effective sting lengths of 3.55 of the reference length. Increasing the ratio of sting diameter to reference length to 0.53 influences damping considerably at angles of attack from 0 to 3 deg at all Reynolds numbers but shows little or no effect at higher angles. Free-flight model wake geometries (wake neck position and size) correlate well with those from captive model tests with the small diameter sting; this adds confidence to obtaining damping derivatives through captive model testing. The damping characteristics of an early Viking configuration obtained on 11.23 and 4.35% scale models using forced and free oscillation test methods, respectively, in two different test facilities are compared. The agreement is quite good under test conditions.
Wind tunnel tests of aerodynamic damping of a launch vehicle
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Improving aerodynamic models for adverse loss-of-control conditions in flight is an area being researched under the NASA Aviation Safety Program. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. As more general aerodynamic models are studied that include nonlinear higher order effects, the possibility of measurements that confound aerodynamic and structural responses are probable. In this study an initial step is taken to look at including structural flexibility in analysis of rigid-body forced-oscillation testing that accounts for dynamic rig, sting and balance flexibility. Because of the significant testing required and associated costs in a general study, it makes sense to capitalize on low cost analytical methods where possible, especially where structural flexibility can be accounted for by a low cost method. This paper provides an initial look at using linear lifting surface theory applied to rigid-body aircraft roll forced-oscillation tests.
As unmanned air vehicles (UAVs) continue to expand their flight envelopes into areas of high angular rate and high angle of attack, modeling the complex unsteady aerodynamics for simulation in these regimes has become more difficult using traditional methods. The goal of this experiment was to improve the current six degree-of-freedom aerodynamic model of a small UAV by replacing the analytically derived damping derivatives with experimentally derived values. The UAV is named the Free-flying Aircraft for Sub-scale Experimental Research, FASER, and was tested in the NASA Langley Research Center 12- Foot Low-Speed Tunnel. The forced oscillation wind tunnel test technique was used to measure damping in the roll and yaw axes. By imparting a variety of sinusoidal motions, the effects of non-dimensional angular rate and reduced frequency were examined over a large range of angle of attack and side-slip combinations. Tests were performed at angles of attack from -5 to 40 degrees, sideslip angles of -30 to 30 degrees, oscillation amplitudes from 5 to 30 degrees, and reduced frequencies from 0.010 to 0.133. Additionally, the effect of aileron or elevator deflection on the damping coefficients was examined. Comparisons are made of two different data reduction methods used to obtain the damping derivatives. The results show that the damping derivatives are mainly a function of angle of attack and have dependence on the non-dimensional rate and reduced frequency only in the stall/post-stall regime
The longitudinal aerodynamic derivatives of the F-8 aircraft with supercritical wing were obtained from flight data by a parameter-extraction algorithm at Mach numbers of 0.8, 0.9, and 0.98. A set of derivatives were obtained from which calculated aircraft responses were correlated almost identically with actual flight responses. In general, the trends of the extracted derivatives obtained by the algorithm agreed with those obtained by a Newton-Raphson method and with preliminary data from the Langley 8-foot transonic pressure tunnel. The wind-tunnel damping derivatives were, however, substantially higher than the converged damping derivatives possibly because of Reynolds number differences between flight and model tests.
A novel wind-tunnel apparatus is described with which all the 12 static and dynamic moment derivatives due to pitching and yawing can be obtained at angles of attack up to 40 deg and in the presence of some sideslip. The experimental technique and the data reduction procedure are discussed, and preliminary data on dynamic derivatives for an aircraft-like configuration at M ? 0.70 are presented. It is shown that in the range of angle of attack investigated, some rather large variations occur in both the two direct damping derivatives and some of the dynamic cross-derivatives; the latter, however, remain small as compared to the corresponding direct damping derivatives (in general less than 10%).
Aerodynamic force and moment equations are developed for 6-DOF missile simulations of both the ascent phase of flight and a tumbling re-entry. The missile coordinate frame (M frame) and a frame parallel to the M frame were used for formulating the aerodynamic equations. The missile configuration chosen as an example is a cylinder with fixed fins and a nose cone. The equations include both the static aerodynamic coefficients and the aerodynamic damping derivatives. The inclusion of aerodynamic damping is essential for simulating a tumbling re-entry. Appended information provides insight into aerodynamic damping.
Time accurate solutions of the Euler and Navier{Stokes equations are used as an approach to elucidate aerodynamic coefficients that include rigid body motion effects. The Army-Navy Finner geometry is used for work flow development due to its simple shape, inexpensive grid generation, and available literature that include aerodynamic damping derivatives obtained from ight test, wind tunnel tests, and computational fluid dynamics. Supersonic conditions for pitch and roll damping include angles of attack up to 90 deg. Aerodynamic responses due to rigid body maneuvers with prescribed wind incidence angles and body rates are computed using the DoD CREATE Kestrel and NASA FUN3D flow solvers. First, reference numerical and experimental results provide validation of aero- dynamic damping terms computed by traditional periodic motion in roll and pitch. Next, individual, impulse motion inputs provide the canonical responses for general input-output modeling based on classical superposition and convolution concepts. Finally, simultaneous impulse excitation of all inputs provides an efficient system identification training scenario for accurate aerodynamic model construction in state space via the NASA Sys- tem/Observer/Controller Identification Toolbox.
rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for component-loaded curved orthogrid panels typical of launch vehicle skin structures. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was applied to correlate the measured input sound pressures across the energized panel. This application quantifies the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software developed for the RPTF method allows easy replacement of the diffuse acoustic field with other pressure fields such as a turbulent boundary layer (TBL) model suitable for vehicle ascent. Structural responses using a TBL model were demonstrated, and wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this environment. Finally, design load factors were developed from the measured and predicted responses and compared with those derived from traditional techniques such as historical Mass Acceleration Curves and Barrett scaling methods for acreage and component-loaded panels.
A rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for a curved orthogrid panel typical of launch vehicle skin structures. Several test article configurations were produced by adding component equipment of differing weights to the flight-like vehicle panel. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was employed to describe the assumed correlation of phased input sound pressures across the energized panel. This application demonstrates the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software modules developed for the RPTF method can be easily adapted for quick replacement of the diffuse acoustic field with other pressure field models; for example a turbulent boundary layer (TBL) model suitable for vehicle ascent. Wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this type of environment. Finally, component vibration environments for design were developed from the measured and predicted responses and compared with those derived from traditional techniques such as Barrett scaling methods for unloaded and component-loaded panels.
Comparison of damping derivatives and wind tunnel data of structural bending modes of Saturn 1
Users manual for a U.S.A. FORTRAN 4 computer program which determines boundary conditions for a thin wing lifting surface program is described. This program, the geometry program, and several other programs are used together in the analysis of lifting, thin wings in steady, subsonic flow according to a kernel function lifting surface theory. The program calculates specific types of boundary conditions automatically such as those necessary to determine pitch and roll damping derivatives. The program also accepts descriptions of the camber or downwash and twist in the form of tables and/or coefficients of equations. The program performs interpolations so that tables and/or coefficients can apply at stations selected by the user and not at stations dictated by the control point locations.
Intense bursts of Langmuir waves with electric fields of 50 to 500 mV / m have been frequently observed at altitudes greater than 500 km in the auroral ionosphere. These bursts are driven by 20 eV to 4 keV field-aligned electrons, which are embedded in an approximately isotropic nonthermal tail of scattered electrons. The Langmuir bursts are often observed at altitudes where the ionosphere is moderately magnetized (OMEGA (sub e) approximately equals omega (sub pe)). Both the moderate magnetization and the scattered electrons have a major influence on the linear dispersion and damping of Langmuir waves. In particular, the linear dispersion is topologically different depending on whether the magnetic field is subcritical (OMEGA (sub e) less than omega (sub pe)) or supercritical (OMEGA (sub e) greater than omega (sub pe)). The correct dispersion and damping can account for the observed polarization of the Langmuir waves, which is very nearly parallel to the geomagnetic field. Inferred properties of the linear instability driven by the field-aligned electrons are discussed. The linear dispersion and damping derived here provide the basis for a nonlinear turbulence study described in a companion paper (Newman et al., this issue).
The effect of modal truncation on the damping ratio and their derivatives with respect to an added mass is investigated for a simply supported, multispan beam with a linear quadratic Gaussian control system. It is found that both the damping ratios and derivatives converge slowly, but the derivatives converge more slowly than the damping ratios. However, it is shown that when Ritz vectors corresponding to static displacements due to actuator forces are added to the reduced model, the convergence of both the damping ratios and their derivatives is accelerated. It is also shown that the accuracy of the damping ratio predicted by a reduced-model control design can be improved significantly if the Ritz vectors are included in the design of the control system. Thus, it appears that Ritz vectors added to the reduced model of flexible structures can improve greatly the accuracy of both the design and analysis of the control system.
A method is derived for calculating the damping coefficients in pitch and roll for a series of triangular wings and a restricted series of sweptback wings at supersonic speeds. The elementary "supersonic source" solution of the linearized equation of motion is used to find the potential function of a line of doublets, and the flows are obtained by surface distributions of these doublet lines. The damping derivatives for triangular wings are found to be a function of the ratio of the tangent of the apex angle to the tangent of the Mach angle. As this ratio becomes equal to and greater than 1.0 for triangular wings, the damping derivatives, in pitch and in roll, become constant. The damping derivative in roll becomes equal to one-half the value calculated for an infinite rectangular wing, and the damping derivative in pitch for pitching about the apex becomes equal to 3.375 times that of an infinite rectangular wing.
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