Trapezoidal Wing Research Articles

Validation of computed high-lift flows with significant wind-tunnel effects

The modeling requirements for validating Navier-Stokes computations of a high-lift trapezoidal wing are investigated. This wing has a full-span slat and a full-span flap and has been tested extensively in the NASA Langley 14 x 22-ft Wind Tunnel and the NASA Ames 12-ft Pressure Wind Tunnel. Because of the size of the wing, there are significant facility effects in the data from the 12-ft wind tunnel. Computational models of the test facility of differing fidelity are developed and tested. Results are compared with experimental lift, drag, and surface pressures. In the computations a simplified, inviscid model of the test section performs as well as a high-fidelity, viscous test-section model. Computed results generally compare very well with experimental data at all but the highest angles of attack. A comparison of computational results from both free-air and wind-tunnel simulations at the same lift condition indicates that it is necessary to simulate the wind tunnel to perform validation using the 12-ft wind-tunnel experimental data

Modal Response of Trapezoidal Wing Structures Using Second-Order Shape Sensitivities

The modal response of wing structures is very important for assessing their dynamic response including dynamic aeroelastic instabilities. Moreover, in a recent study an efficient structural optimization approach was developed using structural modes to represent the static aeroelastic wing response (both displacement and stress). In this paper, the modal response of general trapezoidal wing structures is approximated using shape sensitivities up to the 2nd order. Also different approaches of computing the derivatives are investigated.

Modal response of trapezoidal wing structures using second-order shape sensitivities

Modal response of trapezoidal wing structures using second-order shape sensitivities

ANALYTIC SENSITIVITIES IN COMPOSITE WING-SHAPE SYNTHESIS PART ONE.: PANEL BUCKLING CONSTRAINTS

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials proved to be efficient tools for structural modeling of wings in the preliminary design stage. This paper describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for terms of the stiffness and geometric stiffness matrices without the need to perform numerical integration. The explicit expressions for the terms of the stiffness and geometric stiffness matrices are used for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation based on Ritz analysis using simple polynomials leads to explicit (axpressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber orientations, and panel shape. Integration of the resulting buckling analysis based on the equivalent plate approach is discussed. To assess the new capability, test cases were chosen to address the convergence rate with increased polynomial order, the accuracy of analysis results for panels of general shape and the integration of wing box structural analysis with panel buckling analysis for fast structural analysis of airplane wings.

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.

Status review of a supersonically biased fighter wing design study

Results from an ongoing supersonically-biased fighter wing-design study are summarized. The study has been conducted to explore the effects of supersonic aerodynamic performance, transonic maneuvering, low-speed/high angle-of-attack characteristics, and airframe system integration requirements on fighter aircraft wing design. The approach adopted involves the theoretical and experimental investigation of four advanced aircraft configurations which differ only in wing geometry. Supersonic and low-speed/high angle-of-attack wind tunnel results have been obtained for 20 deg trapezoidal, 65 deg delta, 70/30-deg advanced cranked, and 70/66-deg advanced cranked wing configurations. The supersonic data show that the advanced cranked wings outperform the trapezoidal and delta wings at cruise and moderate lift conditions. Low-speed/high angle-of-attack results show that all wings have significant stability problems above an angle of attack of 20 deg. Aircraft sizing analysis results show that the advanced cranked-wing configurations are significantly lighter, based upon take-off gross weight, than either the trapezoidal or the delta wings.

Analysis of Strake Vortex Breakdown Characteristics in Relation to Design Features

This paper describes a water-tunnel study of the vortex breakdown characteristics of a large number of analytically designed vortex strakes tested in combination with a moderate-aspect-ratio trapezoidal wing. A wide range of strake sizes and slenderness ratios are covered, and examples of the effects of the primary design parameters of size, span, and slenderness on the vortex breakdown characteristics are presented and analyzed in relation to the three-dimensional leading-edge suction distributions. Several examples of detailed planform shaping on strakes of the same general size and slenderness are shown. From these it is demonstrated that vortex stability can be improved by satisfying the design criterion. The criterion states that those shapes having leadingedge suction distributions which increase more rapidly near, and have a higher value at, the spanwise tip of the strake promote vortex stability. A AD b C c cr ( cr ) w cs ED Kv / p

Methods for Calculating the Flow in the Trefftz-Plane Behind Supersonic Wings

By means of the linearized nonviscous theory, methods are developed, using the complex functions of conical flow, for finding downwash and sidewash in the Trefftz-plane—i.e., a t an infinite distance downstream, behind a supersonic wing. Equations are derived which describe this flow field behind several types of flat plate wings: the wide delta wing, the trapezoidal wing (wide delta wing with cutoff tips), and the delta control surfaces (a narrow delta wing, the two sides of which are deflected differentially). Graphs are included which show the results for these cases.

Linearized supersonic aerofoil theory part II

The operational approach to linearized supersonic aerofoil problems is further developed. In particular, the method is extended to give a general treatment of the drag on swept-back wings at zero incidence. Problems involving the lift on swept-back wings are also considered, and a recurrence method developed for obtaining the lift on a trapezoidal wing with tips swept back beyond the Mach angle. As a particular case this latter method is applied to the arrow-head wing.