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The lift on a bent, flat plate is calculated exactly by the use of conformal mapping. Results are presented in terms permitting direct determination of the angle of zero lift, the lift coefficient, and the lift-curve slope for any flap-chord ratio, flap-deflection angle, and angle of attack.
This paper presents a transonic correction method for obtaining dynamic stability derivatives for flight dynamic stability analysis. The method provides a transonic correction to the Theodorsen's theory of unsteady aerodynamics using FUN3D CFD solver of unsteady Reynolds-averaged Navier-Stokes equations (RANS) for a series of wing sections of the Mach 0.745 Transonic Truss-Braced Wing in pitch and plunge oscillations. Unsteady lift and pitching moment coefficients are obtained and used to develop the correction terms in the Theodorsen's theory to account for transonic aerodynamics. The unsteady lift and pitching moment derivatives with respect to the unsteady angle of attack are obtained as frequency response functions of the reduced frequency. These frequency response functions are used to compute the dynamic stability derivatives of lift and pitching moment due to the angle of attack and pitch rate and the dynamic stability derivatives for the rolling moment and yawing moment with respect to the roll rate and yaw rate. A transonic correction is applied to steady-state stability derivatives computed by VSPAERO solver using transonic small disturbance code TSFOIL coupled to an integral boundary method. A dynamic stability analysis is conducted for longitudinal and lateral-directional motions. Without transonic corrections and dynamic stability derivatives, the analysis indicates an unstable phugoid mode. The transonic correction applied to the steady-state stability derivatives computed by VSPAERO shows a stable phugoid mode. This is due to the increase of the drag stability derivatives as a result of the additional wave drag contribution in transonic flow. The effect of the transonic dynamic stability derivatives is observed to be a significant contributor to the increase in the damping values of all the flight dynamic modes of the Mach 0.745 Transonic-Truss Braced Wing.
This paper presents a modeling approach for dynamic aeroelastic flight dynamic analysis of the Mach0.745 Transonic Truss-Braced Wing. The modeling approach is based on a transonic correction method to correct the Theodorsen’s theory for transonic flow. CFD unsteady Reynolds-averaged Navier-Stokes equations (RANS) simulations are conducted using FUN3D solver for a series of wing sections from the Mach 0.745Transonic Truss-Braced Wing in pitch and plunge oscillations. Unsteady lift and pitching moment coefficients are obtained and used to develop the correction terms in the Theodorsen’s theory to account for transonic aerodynamics. The unsteady lift and pitching moment derivatives with respect to the unsteady angle of attack are obtained as functions of the reduced frequency. These derivatives are used to compute the unsteady lift and pitching moment contributions by the angle of attack, pitch rate, and roll rate. They are then approximated using a frequency-domain regression to obtain the dynamic stability derivatives for the Mach 0.745 Transonic Truss-Braced Wing. The structural dynamic mode shapes of the Mach 0.745 TTBW are extracted from a NAS-TRAN finite-element model. These mode shapes are used to compute the generalized unsteady aerodynamic forces. The aerodynamic mass, damping, and stiffness and the aerodynamic lag states are constructed to couple the dynamic aeroelastic contribution to the flight dynamic model of the Mach 0.745 Transonic Truss-Braced Wing. The coupled dynamic aeroelastic flight dynamic equations of motion are formulated. The eigenvalues of the coupled system are computed. All the flight dynamic modes and structural dynamic modes are stable at Match 0.745. The effect of transonic aerodynamics generally causes all the dynamic modes to have lower damping values
Discontinuous wing leading-edge droop designs have been evaluated as a means of modifying wing autorotative characteristics and thus improving airplane spin resistance. Addition of a discontinuous outboard wing leading-edge droop to three typical light airplanes having NACA 6-series wing sections produced significant improvements in stall characteristics and spin resistance. Wind tunnel tests of two wings having advanced natural laminar flow airfoil sections indicated that a discontinuous leading-edge droop can delay the onset of autorotation at high angles of attack without adversely affecting the development of laminar flow at cruise angles of attack.
Data for speeds from Mach 0.50 to Mach 0.99 are presented for configurations with and without fuselage area-rule additions, with and without leading-edge vortex generators, and with and without boundary-layer trips on the wing. The wing pressure coefficients are tabulated. Comparisons between the airplane and model data show that higher second velocity peaks occurred on the airplane wing than on the model wing. The differences were attributed to wind tunnel wall interference effects that caused too much rear camber to be designed into the wing. Optimum flow conditions on the outboard wing section occurred at Mach 0.98 at an angle of attack near 4 deg. The measured differences in section drag with and without boundary-layer trips on the wing suggested that a region of laminar flow existed on the outboard wing without trips.
Noise data were obtained with a small scale model stationary STOL configuration that used an eight lobe mixer nozzle with deflector mounted above a 32-cm-chord wing section. The factors varied to determine their effect upon the noise were wing flap angle, nozzle shape, nozzle location, deflector configuration, and jet velocity. The noise from the mixer nozzle model was compared to the noise from a model using a circular nozzle of the same area. The mixer nozzle model was quieter at the low to middle frequencies, while the circular nozzle was quieter at high frequencies. The perceived noise level (PNL) was calculated for an aircraft 10 times larger than the model. The PNL at 500 feet for the mixer nozzle turned out to be within 1 db of the PNL for the circular nozzle. For some configurations at highly directional broadband noise, which could be eliminated by changes in nozzle and/or deflector location, occurred below the wing.
The results are described of a theoretical study of viscous drag reduction schemes for potential application to the fuselage of a long-haul subsonic transport aircraft. The schemes which were examined included tangential slot injection on the fuselage and various synergetic combinations of tangential slot injection and distributed suction applied to wing and fuselage surfaces. Both passive and mechanical (utilizing turbo-machinery) systems were examined. Overall performance of the selected systems was determined at a fixed subsonic cruise condition corresponding to a flight Mach number of free stream M = 0.8 and an altitude of 11,000 m. The nominal aircraft to which most of the performance data was referenced was a wide-body transport of the Boeing 747 category. Some of the performance results obtained with wing suction are referenced to a Lockheed C-141 Star Lifter wing section. Alternate designs investigated involved combinations of boundary layer suction on the wing surfaces and injection on the fuselage, and suction and injection combinations applied to the fuselage only.
This investigation has a double object: 1) the calculation of the general characteristics of certain wings with progressively varying sections; 2) the determination of data furnishing, in certain cases, some information on the actual distribution of the external forces acting on a wing. We shall try to show certain advantages belonging to the few wing types of variable section which we shall study and that, even if the general aerodynamic coefficients of these wings are not often clearly superior to those of certain wings of uniform section, the wings of variable section nevertheless have certain advantages over those of uniform section in the distribution of the attainable stresses.
The structural effects of nonuniform temperature distributions, such as those produced by aerodynamic heating or thermal ice-prevention systems, are discussed and found to be of two types: The introduction of thermal stresses and distortions as a result of restrained thermal expansion and a change in the stresses and distortions produced by the applied loads as a result of the variation of elastic properties of materials with temperature. These effects are illustrated by sample analyses of the stress and distortion distributions of simple box beams and by calculation of the stresses on a typical wing section.
A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.
The author argues that because of a general misunderstanding of the principles of flight at low speed, there are a large number of airplanes that could be made to fly several miles per hour slower than at present by making slight modifications. In order to show how greatly the wing section affects the minimum speed, curves are plotted against various loadings. The disposition of wings on the airplane slightly affects the lift coefficient, and a few such cases are discussed. Another factor that has an effect on minimum speed is the extra lift exerted by the slip stream on the wings. Also discussed are procedures to be followed by the pilot, especially with regard to stick movements during low speed flight. Also covered are stalling, yaw, rolling moments, lateral control, and the effectiveness of ailerons and rudders.
An inviscid model for the interaction between a thin wing and a nearly uniform propeller slipstream is presented. The model allows the perturbation velocities due to the interaction to be potential although the undisturbed slipstream velocity is rotational. A finite difference scheme is used to solve the governing equation. Numerical examples indicate that the slipstream has a strong effect on the aerodynamic properties of the wing section within the slipstream and lesser effects elsewhere. The slipstream swirling motion strongly affects the wing load distribution, however, its effect on the wing's total lift and wave drag is small. The axial velocity increment in the slipstream has a small effect on the wing lift, however, it causes a large increase in wave drag.
Two different classes of missile aeroprediction programs have been recently developed. The first class of programs provides rapid engineering predictions and includes MISSILE1 and MISSILE2 applicable to missile configurations with axisymmetric bodies. The second class of programs consists of the DEMON series, including a simplified version NSWCDM, designed to calculate detailed loadings acting on supersonic missiles which may have non-circular body cross sections. Both classes account for high angles of attack and track vortices from canard or wing section to the tail section. Extensive comparisons with experimental data are presented including nonlinear effects of canard control.
These experiments were carried out to determine the aerodynamic characteristics of various triplanes, which differed in the relative positions of the wings and, more especially, in the stagger, and in the shape of the wing sections. The tests were restricted to such dispositions as appeared constructively adapted to the plan form considered. Four different sets of wings were used in these tests, three of which had the same cross-section but differed in aspect ratio and in area. The tests were made at an air velocity of about 30 m.p.s. (98.4 ft/sec.) in the large wind tunnel. Results are given in tabular and graphical form.
MVL-15 is the most recent version of the Modified Vortex-Lattice (MVL) code developed within the Aerodynamics Systems Analysis Branch (ASAB) at NASA LaRC. The term "modified" refers to the primary modification of the core vortex-lattice methodology: inclusion of viscous aerodynamics tables that are linked to the linear solution via iterative processes. The inclusion of the viscous aerodynamics inherently converts the MVL-15 from a purely analytic linearized method to a semi-empirical blend which retains the rapid execution speed of the linearized method while empirically characterizing the section aerodynamics at all spanwise lattice points. The modification provides a means to assess non-linear effects on lift that occur at angles of attack near stall, and provides a means to determine the drag associated with the application of design strategies for lift augmentation such as the use of flaps or blowing. The MVL-15 code is applicable to the analyses of aircraft aerodynamics during cruise, but it is most advantageously applied to the analysis of aircraft operating in various high-lift configurations. The MVL methodology has been previously conceived and implemented; the initial concept version was delivered to the ASAB in 2001 (van Dam, C.), subsequently revised (Gelhausen, P. and Ozoroski, T. 2002 / AVID Inc., Gelhausen, P., and Roberts, M. 2004), and then overhauled (Ozoroski, T., Hahn, A. 2008). The latest version, MVL-15 has been refined to provide analysis transparency and enhanced to meet the analysis requirements of the Environmentally Responsible Aviation (ERA) Project. Each revision has been implemented with reasonable success. Separate applications of the methodology are in use, including a similar in-house capability, developed by Olson, E. that is tailored for structural and acoustics analyses. A central premise of the methodology is that viscous aerodynamic data can be associated with analytic inviscid aerodynamic results at each spanwise wing section, thereby providing a pathway to map viscous data to the inviscid results. However, a number of factors can sidetrack the analysis consistency during various stages of this process. For example, it should be expected that the final airplane lift curve and drag polar results depend strongly on the geometry and aerodynamics of the airfoil section; however, flap deflections and flap chord extensions change the local reference geometry of the input airfoil, the airplane wing, the tabulated non-dimensional viscous aerodynamics, and the spanwise links between the linear and the viscous aerodynamics. These changes also affect the bound circulation and therefore, calculation and integration of the induced angle of attack and induced drag. MVL-15 is configured to ensure these types of challenges are properly addressed. This report is a comprehensive manual describing the theory, use, and validation of the MVL-15 analysis tool. Section 3 summarizes theoretical, procedural, and characteristic features of MVL-15, and includes a list of the files required to setup, execute, and summarize an analysis. Section 4, Section 5, Section 6, and Section 7 combine to comprise the User's Guide portions of this report. The MVL-15 input and output files are described in Section 4 and Section 5, respectively; the descriptions are supplemented with example files and information about the file formats, parameter definitions, and typical parameter values. Section 6 describes the Wing Geometry Setup Utility and the 2d-Variants Utility files that simplify and assist setting up a consistent set of MVL-15 geometry and aerodynamics input parameters and input files. Section 7 describes the use of the 3d-Results Presentation Utility file that can be used to automatically create summary tables and charts from the MVL-15 output files. Section 8 documents the Validation Results of an extensive and varied validation test matrix, including results of an airplane analysis representative of the ERA Program. A start-to-finish example of the airplane analysis procedure is described in Section 7.
There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed.
Equations are presented with which to determine spar cross-sections.
A full scale engine wing shielding investigation was conducted at the Lewis Research Center using a 97,900-N (22,000 lb) thrust turbofan engine and a simulated wing section sized around a conventional-take-off type four-engine narrow body airplane. Sound data were obtained for the wing placed at seven positions in a plane parallel to the engine axis, and were compared to data obtained without the wing at both take off and approach power. In addition, the engine was operated with and without extensive acoustic treatment, including a sonic inlet in order to evaluate wing shielding effectiveness with a highly suppressed engine. The wing shielding effectiveness was also calibrated using a 3.8 cm diam air nozzle as a second source. Results indicated that even though about 10 dB broad band shielding was achieved, the equivalent flyover noise reduction was less than 3.0 EPNdB for most configurations.