Graphical method of obtaining theoretical lift distributions on thin wings at supersonic speeds
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THEORIES - FLOW SUPERSONIC↗
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EFFECTS OF WING VERTICAL LOCATION ON THE STABILITY AND CONTROL CHARACTERISTICS AT A MACH NUMBER OF 2.01 OF A CANARD AIRPLANE CONFIGURATION WITH A TRAPEZOIDAL ASPECT-RATIO-3 WING
Effects of wing vertical location on stability and control of canard aircraft at supersonic speeds
AIRCRAFT CONTROL↗
The Rolling Moment Due to Sideslip of Triangular, Trapezoidal, and Related Plan Forms in Supersonic Flow
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WINGS, RECTANGULAR↗
Calculation of wing spars of variable cross-section and linear load
The calculation of wing spars of constant cross-section and load has been thoroughly treated by a large number of authors. Such is not the case,however, regarding the calculation of wing spars whose section and linear load diminish toward the ends, as in wings of trapezoidal contour and decreasing section.
SPARS↗
The use of linearized-aerodynamics and vortex-flow methods in aircraft design /invited paper/
This paper deals with selected linearized-aerodynamic and vortex-flow methods as applied to aircraft design problems at high subsonic speeds. In particular, the NASA Vortex Lattice and Modified Multhopp methods are the linearized techniques employed, and the suction analogy is used to provide estimates associated with vortex-flow aerodynamics. Many examples are given as to how researchers at Langley have used these methods to design the high subsonic, wing-mean-camber shapes for various configurations such as a supersonic transport, high-aspect-ratio transport, trapezoidal fighter wing, strake wing, tandem wing, joined wing, delta wing, and slender cranked wing. Many of these have been built, tested, and have had their data compared with theory. In addition, a technique for defining efficiently performing strake planforms for use in strake-wing combinations is discussed, and further improvements in wing design are outlined. The latter may be obtained by using higher-ordered linear panel methods as well as nonlinear-transonic methods.
Lamar, J. E.↗
A finite-step method for estimating the spanwise lift distribution of wings in symmetric, yawed, and rotary flight at low speeds
The finite-step method was programmed for computing the span loading and stability derivatives of trapezoidal shaped wings in symmetric, yawed, and rotary flight. Calculations were made for a series of different wing planforms and the results compared with several available methods for estimating these derivatives in the linear angle of attack range. The agreement shown was generally good except in a few cases. An attempt was made to estimate the nonlinear variation of lift with angle of attack in the high alpha range by introducing the measured airfoil section data into the finite-step method. The numerical procedure was found to be stable only at low angles of attack.
Krenkel, A. R.↗
Theoretical distribution of lift on thin wings at supersonic speeds : (an extension)
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PRESSURE DISTRIBUTION - AIRFOILS, THIN↗
Flow visualization studies of a general research fighter model employing a strake-wing concept at subsonic speeds
A systematic wind tunnel study was conducted in the Langley high-speed 7 by 10 foot tunnel to document, by oil-flow photographs, the surface flow patterns for configurations incorporating strake-wing geometries indicative of current and proposed maneuvering aircraft. The configurations employed combinations of strakes with reflexed planforms having exposed spans of 10 percent, 20 percent, and 30 percent of the reference wing span and wings with trapezoidal planforms having leading-edge sweep angles of approximately 30 deg, 44 deg, and 60 deg. Tests were conducted at Mach numbers of 0.3 and 0.5 and at angles of attack ranging from approximately 5 deg to 30 deg in 5 deg increments at 0 deg sideslip. The configurations incorporating the strake-wing geometries exhibited more organized flow patterns with smaller asymmetries to higher angles of attack than the corresponding configurations incorporating the wing-alone geometries did.
Luckring, J. M.↗
Subsonic longitudinal and lateral aerodynamic characteristics for a systematic series of strake-wing configurations
A systematic wind tunnel study was conducted in the Langley 7 by 10 foot high speed tunnel to help establish a parametric data base of the longitudinal and lateral aerodynamic characteristics for configurations incorporating strake-wing geometries indicative of current and proposed maneuvering aircraft. The configurations employed combinations of strakes with reflexed planforms having exposed spans of 10%, 20%, and 30% of the reference wing span and wings with trapezoidal planforms having leading edge sweep angles of approximately 30, 40, 44, 50, and 60 deg. Tests were conducted at Mach numbers ranging from 0.3 to 0.8 and at angles of attack from approximately -4 to 48 deg at zero sideslip.
Luckring, J. M.↗
Supersonic aerodynamic characteristics of canard, tailless, and aft-tail configurations for 2 wing planforms
Aerodynamic characteristics of canard, tailless, and aft tail configurations were compared in tests on a general research model (generic fuselage without canopy, inlets, or vertical tails) at Mach 1.60 and 2.00 in the Langley Unitary Plan Wind Tunnel. Two uncambered wing planforms (trapezoidal with 44 deg leading edge sweep and delta with 60 deg leading edge sweep) were tested for each configuration. The relative merits of the configurations were also determined theoretically, to evaluate the capabilities of a linear theory code for such analyses. The canard and aft tail configurations have similar measured values for lift curve slope, maximum lift drag ratio, and zero lift drag. The stability decrease as Mach number increases is greatest for the tailless configuration and least for the canard configuration. Because of very limited accuracy in predicting the aerodynamic parameter increments between configurations, the linear theory code is not adequate for determining the relative merits of canard, tailless, and aft tail configurations.
Covell, P. F.↗
Aerodynamic sensitivities from subsonic, sonic and supersonic unsteady, nonplanar lifting-surface theory
The technique of implicit differentiation has been used in combination with linearized lifting-surface theory to derive analytical expressions for aerodynamic sensitivities (i.e., rates of change of lifting pressures with respect to general changes in aircraft geometry, including planform variations) for steady or oscillating planar or nonplanar lifting surfaces in subsonic, sonic, or supersonic flow. The geometric perturbation is defined in terms of a single variable, and the user need only provide simple expressions or similar means for defining the continuous or discontinuous global or local perturbation of interest. Example expressions are given for perturbations of the sweep, taper, and aspect ratio of a wing with trapezoidal semispan planform. In addition to direct computational use, the analytical method presented here should provide benchmark criteria for assessing the accuracy of aerodynamic sensitivities obtained by approximate methods such as finite geometry perturbation and differencing. The present process appears to be readily adaptable to more general surface-panel methods.
Yates, E. Carson, Jr.↗
Boundary-integral method for calculating aerodynamic sensitivities with illustration for lifting-surface theory
The technique of implicit differentiation has been used in combination with linearized lifting-surface theory to derive analytical expressions for aerodynamic sensitivities (i.e., rates of change of lifting pressures with respect to general changes in aircraft geometry, including planform variations) for steady or oscillating planar or nonplanar lifting surfaces in subsonic, sonic, or supersonic flow. The geometric perturbation is defined in terms of a single variable, and the user need only provide simple expressions or similar means for defining the continuous or discontinuous global or local perturbation of interest. Example expressions are given for perturbations of the sweep, taper, and aspect ratio of a wing with trapezoidal semispan planform. The present process appears to be readily adaptable to more general surface-panel methods.
Yates, E. Carson, Jr.↗
Influence of leading-edge suction on lift-drag ratios of wings at supersonic speeds
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WING TIPS, ROUNDED↗
Effects of Horizontal-Control Planform and Wing-Leading-Edge Modification on Low-Speed Longitudinal Aerodynamic Characteristics of a Canard Airplane Configuration
An investigation at low subsonic speeds has been conducted in the Langley 300-MPH 7- by 10-foot tunnel. The basic wing had a trapezoidal planform, an aspect ratio of 3.0., a taper ratio of 0.143, and an unswept 80-percent-chord line. Modifications to the basic wing included deflectable full-span and partial-span leading-edge chord-extensions. A trapezoidal horizontal control similar in planform to the basic wing and a 60 deg sweptback delta horizontal control were tested in conjunction with the wing. The total planform area of each horizontal control was 16 percent of the total basic-wing area. Modifications to these horizontal controls included addition of a full-span chord-extension to the trapezoidal planform and a fence to the delta planform.
Spencer, Bernard, Jr.↗
Longitudinal and Lateral Stability and Control Characteristics of Various Combinations of the Component Parts of Two Canard Airplane Configurations at Mach Numbers of 1.41 and 2.01
An investigation has been conducted in the Langley 4- by 4-foot supersonic pressure tunnel to determine the aerodynamic characteristics in pitch and sideslip of a generalized canard airplane model. Two wings of equal area but differing in plan form were investigated. The model was equipped with a trapezoidal canard surface with an area 12 percent of the wing area, a low-aspect-ratio vertical tail, and twin ventral fins. The interference effects of the canard wake on the wing result in little or no gain in the total lift at a Mach number of 1.41 but at a Mach number of 2.01 a substantial portion of the canard lift is retained with a resultant increase in total lift. Because these interference effects of the canard wake appear to be concentrated near the leading edge of the wing, the proper location of the wing leading edge with respect to the center of moments may result in a substantial increase in the moment increment provided by a canard surface even though the total lift provided by the canard is small. For these configurations the trapezoidal wing retained the most lift and had the largest favorable moment increment produced by the canards. The canard configurations have the same characteristic decrease in directional-stability with angle of attack as most conventional high-fineness-ratio supersonic configurations. Although the presence of the canard surface caused a small increase in the directional stability at a Mach number of 1.41 for the delta-wing configuration, the presence of the canards resulted in small decreases in the directional-stability level at a Mach number of 2.01 for both wing configurations. A canard deflection of 15 deg provides an increase in the positive effective dihedral approximately as large as that provided by the presence of the vertical tail. This effect of canard deflection might complicate the lateral-control problem in the case of a rolling pull-up maneuver.
Driver, Cornelius↗
Lift, Drag, and Pitching Moment of Low-Aspect-Ratio Wings at Subsonic and Supersonic Speeds: Triangular Wing of Aspect Ratio 2 with NACA 0005-63 Thickness Distribution, Cambered and Twisted for a Trapezoidal Span Load Distribution
A wing-body combination having a plane triangular wing of aspect ratio 2 with NACA 0005-63 thickness distribution in streamwise planes, and twisted and cambered for a trapezoidal span load distribution has been investigated at both subsonic and supersonic Mach numbers. The lift, drag, and pitching moment of the model are presented for Mach numbers from 0.60 to 0.90 and 1.30 to 1.70 at a Reynolds number of 3.0 million. The variations of the characteristics with Reynolds number are also shown for several Mach numbers.
Smith, Willard G.↗
Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis
Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.
Livne, Eli↗
Equivalent Skin Analysis of Wing Structures Using Neural Networks
An efficient method of modeling trapezoidal built-up wing structures is developed by coupling. in an indirect way, an Equivalent Plate Analysis (EPA) with Neural Networks (NN). Being assumed to behave like a Mindlin-plate, the wing is solved using the Ritz method with Legendre polynomials employed as the trial functions. This analysis method can be made more efficient by avoiding most of the computational effort spent on calculating contributions to the stiffness and mass matrices from each spar and rib. This is accomplished by replacing the wing inner-structure with an "equivalent" material that combines to the skin and whose properties are simulated by neural networks. The constitutive matrix, which relates the stress vector to the strain vector, and the density of the equivalent material are obtained by enforcing mass and stiffness matrix equities with rec,ard to the EPA in a least-square sense. Neural networks for the material properties are trained in terms of the design variables of the wing structure. Examples show that the present method, which can be called an Equivalent Skin Analysis (ESA) of the wing structure, is more efficient than the EPA and still fairly good results can be obtained. The present ESA is very promising to be used at the early stages of wing structure design.
Liu, Youhua↗