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Computer programs to determine aerodynamic coefficients for Apollo Applications Program vehicles in orbital environment
Maximum likelihood parameter identification is used to estimate the aerodynamic coefficients of a 'flying' aircraft model which is mounted in a transonic wind tunnel by a system of cables and pulleys. The model's motion is governed by both cable and aerodynamic forces, where the parameters to be identified are functions of the aerodynamic forces but cable forces greatly predominate. The test data were successfully processed assuming a linear equation model in the identification procedure. In one instance, the procedure was able to detect a failing measurement instrument. The final parameter estimates are compared to estimates obtained in independent tests of a similar aircraft model.
Some recent experience at Ames Research Center in the estimation of aerodynamic coefficients for the Lear-Jet and the Augmentor Wing Jet STOL Research Aircraft is reviewed. The coefficients estimated from flight data are compared with values based on large-scale wind-tunnel tests. The results obtained by the regression and quasilinearization identification techniques are also compared. The regression method generally provides the lower standard deviation in the coefficient estimates and provides the better fit to the wind-tunnel values. The addition of nonlinear terms in the aerodynamic equations decreases the difference between the estimated and measured time histories but also increases the standard deviation in the estimated coefficient values.
Pressure distributions, aerodynamic coefficients, and shock shapes were measured on blunt bodies of revolution in Mach 6 CF4 and in Mach 6 and Mach 10 air. The angle of attack was varied from 0 deg to 20 deg in 4 deg increments. Configurations tested were a hyperboloid with an asymptotic angle of 45 deg, a sonic-corner paraboloid, a paraboloid with an angle of 27.6 deg at the base, a Viking aeroshell generated in a generalized orthogonal coordinate system, and a family of cones having a 45 deg half-angle with spherical, flattened, concave, and cusp nose shapes. Real-gas effects were simulated for the hperboloid and paraboloid models at Mach 6 by testing at a normal-shock density ratio of 5.3 in air and 12 CF4. Predictions from simple theories and numerical flow field programs are compared with measurement. It is anticipated that the data presented in this report will be useful for verification of analytical methods for predicting hypersonic flow fields about blunt bodies at incidence.
The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.
The errors in the dynamic data output from the Aerodynamic Coefficient Identification Packages (ACIP) flown on Shuttle flights 1, 3, 4, and 5 were determined using the output from the Inertial Measurement Units (IMU). A weighted least-squares batch algorithm was empolyed. Using an averaging technique, signal detection was enhanced; this allowed improved calibration solutions. Global errors as large as 0.04 deg/sec for the ACIP gyros, 30 mg for linear accelerometers, and 0.5 deg/sec squared in the angular accelerometer channels were detected and removed with a combination is bias, scale factor, misalignment, and g-sensitive calibration constants. No attempt was made to minimize local ACIP dynamic data deviations representing sensed high-frequency vibration or instrument noise. Resulting 1sigma calibrated ACIP global accuracies were within 0.003 eg/sec, 1.0 mg, and 0.05 deg/sec squared for the gyros, linear accelerometers, and angular accelerometers, respectively.
The methods by which aerodynamic coefficients are determined and discussed. These include: calculations, wind tunnel experiments and experiments in flight for various prototypes of the Alpha Jet. A comparison of obtained results shows good correlation between expectations and in-flight test results.
Experimental values of shock shapes (alpha = 0 degrees and 10 degrees) and static aerodynamic coefficients (alpha = -4 degrees to 12 degrees) for sharp and spherically blunted cones having cone half-angles of 30, 45, 60, and 70 degrees and nose bluntness ratios of 0, 0.25, and 0.50 are presented. Shock shapes were also measured at 0 degree angle of attack by using a flat-faced cylinder (90 degree cone) and a hemispherically blunted cylinder (sphere). All tests were conducted in helium (gamma = 5/3) at a free-stream Mach number of 20.3 and a unit free-stream Reynolds number of 22,400,000 per meter. Comparisons between measured values and predicted values were made by using several numerical and simple engineering methods.
Experimental values of shock shapes (angles of attack of 0 deg and 10 deg) and static aerodynamic coefficients (angles of attack of -4 deg to 12 deg for sharp and spherically blunted cones having cone half angles of 30 deg, 45 deg, 60 deg, and 70 deg, and nose bluntness ratios of 0, 0.25, and 0.50 are presented. Shock shapes were measured at 0 deg angle of attack by using a flat faced cylinder (90 deg cone) and a hemispherically blunted cylinder (sphere). All tests were conducted in air at a free stream Mach number of 5.9 and a unit free stream Reynolds number of 2,800,000 per meter. Comparisons between measured values and predicted values were made by using several numerical and simple engineering methods.
The problem of the transformation of numerical values expressed in one system of units into another set or system of units frequently arises in connection with aerodynamic problems. Report contains aerodynamic coefficients and conversion tables needed to facilitate such transformation. (author)
The landing accuracy of an autonomous guided parafoil is influenced by its ability to predict the trajectory, which is shaped by the parafoil’s aerodynamic characteristics and atmospheric winds. The parafoil is subjective to imperfections from manufacturing, damage during deployment, lateral asymmetry, and so forth, leading to discrepancies between the actual aerodynamic properties and the onboard aerodynamic model. Thus, by acquiring an accurate knowledge of the aerodynamic properties and real-time winds, the onboard simulation can reduce the undertainties in the dynamics modeling for trajectory propagation to improve the landing accuracy. For that purpose, a non-linear least-squares method is developed to calculate differential corrections for optimizing and extracting the parafoil aerodynamic coefficients and winds on-the-fly using real-time data from the Global Positioning System (GPS). Post-flight analyses from two test flights have shown that the method provides improved simulations that closely match the GPS trajectories.
The development of a nonplanar lifting surface method having a continuous distribution of singularities and satisfying the tangent flow boundary condition on the mean camber surface is given. The method predicts some incompressible longitudinal aerodynamic coefficients of rectangular wings which have circular-arc camber. The solution method is of the integral-equation type and the resulting surface integrals are evaluated by either using numerical or analytical techniques, as are appropriate. Applications are made and the results compared with those from an exact two-dimensional circular-arc camber solution, a three-dimensional flat-wing solution which represents the camber by a projected slope onto the flat surface, and a flat-wing experiment. From these comparisons, the present method is found to predict well the flat-wing experiment and limiting values, in addition to the center of pressure variation at an angle of attack of zero for any camber. For wings having camber ratios larger than about 1.25% and moderate to high aspect ratios, the results deterioriate due to the inadequacy of lifting pressure modes employed.
Closed-form expressions and tables composed from these expressions are presented for complete and partial conic and spheric bodies at combined angles of attack and sideslip in Newtonian flow. Aerodynamic coefficients of these bodies are tabulated for various body segments over a range of angles of attack from 1 deg to 85 deg and angles of sideslip from 0 deg to 15 deg. Some comparisons between Newtonian predictions and hypersonic experimental aerodynamic characteristics were made for conic bodies hawing various surface slopes, nose bluntnesses, and body cross sections to indicate the range of validity of the theory. In general, the theory is shown to agree quite well with experimental results for sharp-nose complete cones and for configurations hawing large blunted noses and steep surface slopes. However, agreement between theory and experiment generally is poor for the more slender, slightly blunted complete or half conic bodies and also for sharp-nose half conic bodies where real-flow phenomena such as forebody interference, viscous forces, leeward surface contributions, or leading-edge pressure reductions may have significant effect. The agreement between theory and experiment for the bodies considered can be improved by using the stagnation pressure coefficient behind a normal shock rather than 2 as the Newtonian coefficient, although for the sharp-nose half conic bodies there i s no theoretical justification for this modification.
Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).
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.
Equations for predicting aerodynamic stability of bodies of revolution with offset centers of gravity at supersonic and hypersonic speeds
A parameter-extraction algorithm was used to determine the lateral aerodynamic derivatives from flight data for the F-8 aircraft with supercritical wing. The flight data used were the recorded responses to aileron or rudder pulses for Mach numbers of 0.80, 0.90, and 0.98. Results of this study showed that a set of derivatives were determined which yielded a calculated aircraft response almost identical with the response measured in flight. Derivatives extracted from motion resulting from rudder inputs were somewhat different from those resulting from aileron inputs. It was found that the derivatives obtained from the rudder-input data were highly correlated in some instances. Those from the aileron input had very low correlations and appeared to be the more reliable.
Flight-test data were used to extract the longitudinal aerodynamic parameters of the F-8C aircraft. The aircraft was trimmed in a steady turn at angles of attack of approximately 9 deg and 13 deg at Mach numbers of 0.7 and 0.8. The parameters extracted resulted in a good match to the flight data and the values obtained were reasonable. The values were further verified by comparing the period and time to damp to half-amplitude, as calculated by using the extracted parameter values, with the period and time to damp to half-amplitude actually measured from the flight data traces. These results show that for the set of data examined, a mathematical model using linear aerodynamics was adequate to describe the response motions at the test angles of attack.