Some Effects of Sweep and Aspect Ratio on the Transonic Flutter Characteristics of a Series of Thin Cantilever Wings Having a Taper Ratio of 0.6
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Flutter analysis of a two degree of freedom airfoil in compressible flow is performed using a state-space representation of the unsteady aerodynamic behavior. Indicial response functions are used to represent the normal force and moment response of the airfoil. The structural equations of motion of the airfoil with bending and torsional degrees of freedom are coupled to the unsteady air loads and the aeroelastic system so modelled is solved as an eigenvalue problem to determine the stability. The aeroelastic equations are also directly integrated with respect to time and the time-domain results compared with the results from the eigenanalysis. A good agreement is obtained. The derivatives of the flutter speed obtained from the eigenanalysis are calculated with respect to the mass and stiffness parameters by both analytical and finite-difference methods for various transonic Mach numbers. The experience gained from the two degree of freedom model is applied to study the sensitivity of the flutter response of a wing with respect to various shape parameters. The parameters being considered are as follows: (1) aspect ratio; (2) surface area of the wing; (3) taper ratio; and (4) sweep. The wing deflections are represented by Chebyshev polynomials. The compressible aerodynamic state-space model used for the airfoil section is extended to represent the unsteady aerodynamic forces on a generally laminated tapered skewed wing. The aeroelastic equations are solved as an eigenvalue problem to determine the flutter speed of the wing. The derivatives of the flutter speed with respect to the shape parameters are calculated by both analytical and finite difference methods.
Lift characteristics and pressure distribution for a NACA 230 wing were investigated for an angle of attack range of from -10 to +24 degrees and Mach range of from 0.2 to 0.7. Maximum lift coefficient increased up to a Mach number of 0.3, decreased rapidly to a Mach number of 0.55, and then decreased moderately. At high speeds, maximum lift coefficient was reached at from 10 to 12 degrees beyond the stalling angle. In high-speed stalls, resultant load underwent a moderate shift outward.
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Low-aspect-ratio wings having pointed plan forms are treated on the assumption that the flow potentials in planes at right angles to the long axis of the airfoils are similar to the corresponding two-dimensional potentials. For the limiting case of small angles of attack and low aspect ratios the theory brings out the following significant properties: (1) The lift of a slender, pointed airfoil moving in the direction of its long axis depends on the increase in width of the sections in a downstream direction. Sections behind the section of maximum width develop no lift. (2) The spanwise loading of such an airfoil is independent of the plan form and approaches the distribution giving a minimum induced drag. (3) The lift distribution of a pointed airfoil travelling point-foremost is relatively unaffected by the compressibility of the air below or above the speed of sound. A best of a triangular airfoil at a Mach number of 1.75 verified the theoretical values of lift and center of pressure.
Contains an outline of investigations dealing with interference effects on the static stability of various airplane configurations that were conducted, were being conducted, and were started at the time of this report. Results of several investigations are presented and discussed briefly. A supplement is attached showing the configurations tested and outlining the various test programs. Suggestions for future investigations are also included.
Contains results of tunnel tests to determine effects of various combinations of split flaps, slats, and nose slats on the stability characteristics of a tapered 37.5 degree sweptback wing of aspect ratio 3 in straight and rolling flow.
The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.
Report presents the results of an investigation conducted to determine some of the effects of airfoil section and washout on the experimental and calculated characteristics of 10-percent-thick wings. Three wings of aspect ratio 9 and ratio of root chord to tip chord 2.5 were tested. One wing had NACA 64-210 sections and 2 degree washout, the second had NACA 65-210 sections and 2 degree washout, and the third had NACA 65-210 sections and 0 degree washout. It was found that the experimental characteristics of the wings could be satisfactorily predicted from calculations based upon two-dimensional data when the airfoil contours of the wings conformed to the true airfoil sections with the same high degree of accuracy as the two-dimensional models.
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A computational parameter study is presented of potential reductions in induced drag and increases in lateral-directional stability due to sheared wing tips attached to an untwisted wing of moderate sweep and aspect ratio. Sheared tips are swept and tapered wing-tip devices mounted in the plane of the wing. The induced-drag results are obtained using an inviscid, incompressible surface-panel method that models the nonlinear effects due to the deflected and rolled-up wake behind the lifting surface. The induced-drag results with planar sheared tips are compared to straight-tapered tip extensions and nonplanar winglet geometries. The lateral-directional static-stability characteristics of the wing with sheared tips are estimated using a quasi-vortex-lattice method. For certain combinations of sheared-tip sweep and taper, both the induced efficiency of the wing and the relevant static-stability derivatives are predicted to increase compared to the wing with a straight-tapered tip modification.
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