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The general basis of the theory of lifting surfaces is discussed. The problem of the flow of a fluid about a lifting surface of infinite span is examined in terms of the existence of vortexes in the current. A general theory of permanent flow is discussed. Formulas for determining the influence of aspect ratio that may be applied to all wings, whatever their plane form, are given.
Wind tunnel studies have been conducted to determine the specific locations of aerodynamic noise production within the flow field about various lifting-surface configurations. The models tested included low aspect ratio shapes intended to represent aircraft flaps, a finite aspect ratio NACA 0012 wing, and a multi-element wing section consisting of a main section, a leading edge flap, and dual trailing edge flaps. Turbulence was induced on the models by surface roughness. Lift and drag were measured for the flap models. Hot-wire anemometry was used for study of the flap-model vortex roll-up. Apparent noise source distributions were measured by use of a directional microphone system, located outside the tunnel, which was scanned about the flow region to be analyzed under computer control. These distributions exhibited a diversity of pattern, suggesting that several flow processes are important to lifting-surface noise production. Speculation concerning these processes is offered.
The problem of potential steady subsonic flow for lifting surfaces is considered. This problem requires the solution of an integral equation relating the value of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface is divided into small (quadrilateral hyperboloidal) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each element and equal to their values at the centroids of the elements. This yields a set of linear algebraic equations. Numerical results are in good agreement with existing ones.
A method is presented for the calculation of lift coefficients for rectangular lifting surfaces of aspect ratios from 0.125 to 10 operating at finite depths beneath the water surface, including the zero depth or planing condition. Theoretical values are compared with experimental values obtained at various depths of submergence with lifting surfaces of aspect ratios from 0.125 to 10. The method can also be applied to hydrofoils with dihedral. Lift coefficients computed by this method are in good agreement with existing experimental data for aspect ratios from 0.125 to 10 and dihedral angles up to 10 degrees.
A method is presented for the calculation of lift coefficients for rectangular lifting surfaces of aspect ratios from 0.125 to 10 operating at finite depths beneath the water surface, including the zero depth or planing condition. Theoretical values are compared with experimental values obtained at various depths of submergence with lifting surfaces of aspect ratios from 0.125 to 10. The method can also be applied to hydrofoils with dihedral. Lift coefficients computed by this method are in good agreement with existing experimental data for aspect ratios from 0.125 to 10 and dihedral angles up to 30 deg.
Flutter analysis for thin lifting surfaces by application of supersonic kernel function procedure
Lifting surfaces supersonic-hypersonic flutter at angle of attack determined by shock expansion, Newtonian flow and local flow piston theory
Deep electrolytic tank as lifting-surface calculator - electric analogy
The problem of lifting surfaces in steady incompressible flow is considered in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential (normal wash) on the lifting surface. The integral equation is approximated by a system of linear algebraic equations obtained by dividing the surfaces into small quadrilateral elements and by assuming the potential discontinuity and the normal wash to be constant within each element. The wake geometry is obtained through iteration by satisfying the condition that the velocity be tangent to the surface of the wake and that the potential discontinuity be constant along the streamlines. Numerical results are in good agreement with existing ones
The aerodynamic ramifications of utilizing three lifting surfaces as opposed to the conventional or canard lifting configurations have been studied on a theoretical basis by previous researchers. This paper presents an experimental investigation of various configuration modifications for an unyawed typical business jet at a Reynolds number of 1.3 million. The three surface has better lift and high-lift drag characteristics than either the canard or tail-aft configurations, but the cruise drag is more. The induced drag at cruise is highest for the canard and lowest for the tail-aft configuration. The pitching moment characteristics are somewhat between those of the canard and tail-aft configurations. A decrease in gap adversely affects the pitching moment characteristics. A smaller stagger leads to better aerodynamic and stability characteristics. A decrease in span of the forward wing gives better cruise drag and longitudinal stability characteristics, but has adverse effects on high-lift drag. A variation in the incidence angles of either or both the forward and aft wings changes the zero-lift moments of the configuration, while marginally affecting overall lift and drag. At cruise, the lift to drag ratio is highest for the conventional and lowest for the three surface. For high lift conditions, the order is reversed.
A new incompressible lifting-surface theory is developed for thin rectangular wings. The solution requires the downwash equation to be in the form of Cauchy-type integrals. Lan's method is employed for the chordwise integrals since it properly accounts for the leading-edge singularity, Cauchy singularity and Kutta condition. The Cauchy singularity in the spanwise integral is also accounted for by using the midpoint trapezoidal rule and theory of Chebychev polynomials. The resulting matrix equation, formed by satisfying the boundary condition at control points, is simpler and quicker to compute than other lifting surface theories. Solutions were found to converge with only a small number of control points and to compare favorably with results from other methods.
This investigation concerns the time and frequency formulations of non-linear two-dimensional lifting surfaces exposed to an incompressible flow field and subjected to an external pressure pulse. In order to address this problem, Volterra series approach in conjunction with the multidimensional Laplace transform is used. This methodology enabling one to solve the aeroelastic governing equations of lifting surfaces opens the way to connect this methodology with that based on neural networks and NARMAX/NARX networks models. Moreover, this extended way to address this problem constitutes a good basis for treatment of the theory of 3D lifting surfaces.
A low frequency unsteady lifting-line theory is developed for a harmonically oscillating wing of large aspect ratio. The wing is assumed to be chordwise rigid but completely flexible in the span direction. The theory is developed by use of the method of matched asymptotic expansions which reduces the problem from a singular integral equation to quadrature. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. The influence of reduced frequency, aspect ratio, planform shape, and mode of oscillation on wing aerodynamics is demonstrated through numerical examples. Compared with lifting-surface theory, computation time is reduced significantly. Using the present theory, the energetic quantities associated with the propulsive performance of a finite wing oscillating in combined pitch and heave are obtained in closed form. Numerical examples are presented for an elliptic wing.
End plates and winglets improve aerodynamic characteristics of aircraft wings and other fixed lifting surfaces. Retractable end plates automatically actuated by same shaft that deflects lifting surface and require little or no extra power and absolutely no control input from cockpit. Besides being modular in construction, easily fitted to any existing aircraft design with only minor modifications.
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.
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.
Users manual for a U.S.A. FORTRAN 4 computer program which determines boundary conditions for a thin wing lifting surface program is described. This program, the geometry program, and several other programs are used together in the analysis of lifting, thin wings in steady, subsonic flow according to a kernel function lifting surface theory. The program calculates specific types of boundary conditions automatically such as those necessary to determine pitch and roll damping derivatives. The program also accepts descriptions of the camber or downwash and twist in the form of tables and/or coefficients of equations. The program performs interpolations so that tables and/or coefficients can apply at stations selected by the user and not at stations dictated by the control point locations.
A computational technique has been developed for performing preliminary design aeroelastic analyses of large aspect ratio lifting surfaces. This technique, applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. An integrating matrix is employed to solve these equations for divergence and flutter eigenvalues and steady aeroelastic deformation. Results are presented for simple examples which verify the technique and demonstrate how it can be applied to analyze lifting surfaces, including those constructed from composite materials.