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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1947

Method for calculating wing characteristics by lifting-line theory using nonlinear section lift data

A method is presented for calculating wing characteristics by lifting-line theory using nonlinear section lift data. Material from various sources is combined with some original work into the single complete method described. Multhopp's systems of multipliers are employed to obtain the induced angle of attack directly from the spanwise lift distribution. Equations are developed for obtaining these multipliers for any even number of spanwise stations, and values are tabulated for 10 stations along the semispan for asymmetrical, symmetrical, and antisymmetrical lift distributions. In order to minimize the computing time and to illustrate the procedures involved, simplified computing forms containing detailed examples are given for symmetrical lift distributions. Similar forms for asymmetrical and antisymmetrical lift distributions, although not shown, can be readily constructed in the same manner as those given. The adaptation of the method for use with linear section lift data is also illustrated. The adaptation has been found to require less computing time than most existing methods.

Sivells, James C↗
NASA NTRS1978

Lifting line theory for transonic flow

Lifting line theory is applied to describe the flow about a lifting wing at transonic speeds. The method extends that of Van Dyke (1975), in which lifting line theory is viewed as a singular perturbation problem, to transonic flows. Inner and outer expansions as the aspect ratio approaches infinity of the transonic small disturbance equations are found. It is shown that the solutions match asymptotically. A boundary value problem is formulated which describes the first aspect ratio correction to the two dimensional cross sectional transonic flow. The theory is especially applicable to wings of similar cross-sections.

Cook, L. P.↗
NASA NTRS1982

Unsteady lifting-line theory with applications

Unsteady lifting-line theory is developed for a flexible unswept wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The theory is formulated in terms of the acceleration potential and treated by the method of matched asymptotic expansions. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. Sample numerical calculations are presented. The present work identifies and resolves errors in the unsteady lifting-line theory of James and points out a limitation in that of Van Holten. Comparison of the results of Reissner's approximate unsteady lifting-surface theory with those of the present work shows favorable agreement. The present work thus provides some formal justification for Reissner's ad hoc theory. For engineering purposes, the region of applicability of the theory in the reduced frequency-aspect ratio domain is identified approximately and found to cover most cases of practical interest.

Ahmadi, A. R.↗
NASA NTRS1989

Correlation of Puma airloads: Lifting-line and wake calculation

A cooperative program undertaken by organizations in the United States, England, France, and Australia has assessed the strengths and weaknesses of four lifting-line/wake methods and three CFD methods by comparing their predictions with the data obtained in flight trials of a research Puma. The Puma was tested in two configurations: a mixed bladed rotor with instrumented rectangular tip blades, and a configuration with four identical swept tip blades. The results are examined of the lifting-line predictions. The better lifting-line methods show good agreement with lift at the blade tip for the configuration with four swept tips; the moment is well predicted at 0.92 R, but deteriorates outboard. The predictions for the mixed bladed rotor configuration range from fair to good. The lift prediction is better for the swept tip blade than for the rectangular tip blade, but the reasons for this cannot be determined because of the unmodeled effects of the mixed bladed rotor.

Bousman, William G.↗
NASA NTRS1985

Unsteady lifting-line theory as a singular-perturbation problem

Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting line theory of James (1975), and points out a limitation in that of Van Holten (1975, 1976, 1977).

Ahmadi, A.↗
NASA NTRS1980

Numerical lifting line theory applied to drooped leading-edge wings below and above stall

A numerical iterative solution to the classical Prandtl lifting-line theory, suitably modified for poststall behavior, is used to study the aerodynamic characteristics of straight rectangular finite wings with and without leading-edge droop. This study is prompted by the use of such leading-edge modifications to inhibit stall/spins in light general aviation aircraft. The results indicate that lifting-line solutions at high angle of attack can be obtained that agree with experimental data to within 20%, and much closer for many cases. Therefore, such solutions give reasonable preliminary engineering results for both drooped and undrooped wings in the poststall region. However, as predicted by von Karman, the lifting-line solutions are not unique when sectional negative lift slopes are encountered. In addition, the present numerical results always yield symmetrical lift distributions along the span, in contrast to the asymmetrical solutions observed by Schairer in the late 1930's. Finally, a series of parametric tests at low angle of attack indicate that the effect of drooped leading edges on aircraft cruise performance is minimal.

Anderson, J. D., Jr.↗
NASA NTRS1981

An asymptotic unsteady lifting-line theory with energetics and optimum motion of thrust-producing 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.

Ahmadi, A. R.↗
NASA NTRS1957

Linearized Lifting-Surface and Lifting-line Evaluations of Sidewash Behind Rolling Triangular Wings at Supersonic Speeds

The lifting-surface sidewash behind rolling triangular wings has been derived for a range of supersonic Mach numbers for which the wing leading edges remain swept behind the mark cone emanating from the wing apex. Variations of the sidewash with longitudinal distance in the vertical plane of symmetry are presented in graphical form. An approximate expression for the sidewash has been developed by means of an approach using a horseshoe-vortex approximate-lifting-line theory. By use of this approximate expression, sidewash may be computed for wings of arbitrary plan form and span loading. A comparison of the sidewash computed by lifting-surface and lifting-line expressions for the triangular wing showed good agreement except in the vicinity of the trailing edge when the leading edge approached the sonic condition. An illustrative calculation has been made of the force induced by the wing sidewash on a vertical tail located in various longitudinal positions.

Bobbitt, Percy J↗
NASA NTRS1996

A Comparison of Lifting-Line and CFD Methods with Flight Test Data from a Research Puma Helicopter

Four lifting-line methods were compared with flight test data from a research Puma helicopter and the accuracy assessed over a wide range of flight speeds. Hybrid Computational Fluid Dynamics (CFD) methods were also examined for two high-speed conditions. A parallel analytical effort was performed with the lifting-line methods to assess the effects of modeling assumptions and this provided insight into the adequacy of these methods for load predictions.

Bousman, William G.↗
NASA NTRS1981

Transonic swept wings studied by the lifting-line theory

Transonic swept wings are analyzed as a lifting-line problem under a small-disturbance approximation. Basic concepts and principal results of the asymptotic theory are discussed. The study focuses on straight oblique wings and V-shaped swept wings, of which the local centerline curvature can be equated to zero. The three-dimensional (3-D) perturbation of the nonlinear component flow admits a similarity flow structure but requires that all wing sections are generated from a single airfoil profile; the reduced 2-D problems in this case are solved only once for all span stations. Examples of solutions involving high subcritical and slightly supercritical component flows are demonstrated and compared with surface pressure data from 3-D computer codes based on the full-potential equation (FLO 22). Except in the neighborhood of leading edges, where the small-disturbance assumption breaks down, and in the vicinities of wing tips and the symmetry plane, where neither the theory nor the 3-D codes may claim full validity, reasonable agreement is consistently found. The explicit results from the upwash analysis, along with the similarity flow structure, provides a rational approach to the control of 3-D effects in transonic aerodynamic design studies.

Cheng, H. K.↗
NASA NTRS1978

Lifting-line theory of oblique wings

The study extends Prandtl's lifting-line theory to planar wings involving swept and curved centerlines. Attention is focused on distinct features of such a theory, with special emphasis on an oblique wing in a steady incompressible potential flow. The analysis presented is compared with exact solutions derived from an inverse method and with results from a panel method.

Cheng, H. K.↗
NASA NTRS1978

Transonic lifting line theory - Numerical procedure for shock-free flows

An algorithm for computing transonic lifting-line theory without shocks is presented; the numerical procedure relies on two-dimensional analyses developed to solve inviscid flow equations for slender airfoils. From a series of solutions to two-dimensional problems in which span effects appear parametrically, the three-dimensional potential field characterization is obtained. Numerical results are given for a lifting wing with an elliptic (spanwise) distribution of chord and a NACA-0012 cross section (a freestream Mach number of 0.63 and an angle of attack of 2 deg are assumed).

Small, R. D.↗
NASA NTRS1943

Limitations of Lifting-Line Theory for Estimation of Aileron Hinge-Moment Characteristics

Hinge-moment parameters for several typical ailerons were calculated from section data with the aspect-ratio correction as usually determined from lifting-line theory. The calculations showed that the agreement between experimental and calculated results was unsatisfactory. An additional aspect-ratio correction, calculated by the method of lifting-surface theory, was applied to the slope of the curve of hinge-moment coefficient against angle of attack at small angles of attack. This so-called streamline-curvature correction brought the calculated and experimental results into satisfactory agreement.

ATI-13584↗
NASA NTRS2017

Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing

This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.

Aeroelasticity↗
NASA NTRS2006

A Note about Self-Induced Velocity Generated by a Lifting-Line Wing or Rotor Blade

This report presents an elementary analysis of the induced velocity created by a field of vortices that reside in the wake of a rotor blade. Progress achieved by other researchers in the last 70 years is briefly reviewed. The present work is presented in four stages of complexity that carry a lifting-line representation of a fixed wing into a single-blade rotor. The analysis leads to the conclusion that the lifting rotor's spiraling vortex wake structure has very high induced power when compared to the ideal wing. For an advanced ratio of one-half, induced power is on the order of 10 times that of the wing when the comparison is made at wingspan equal to rotor diameter and wing and rotor having equal lift.

Harris, Franklin D.↗
NASA NTRS1979

Lifting-line theory of oblique wings in transonic flows

Three-dimensional corrections to the nonlinear mixed flow admitted by a high-aspect-ratio swept wing of practical interest are analyzed by solving a perturbation problem and matching its solution to that of an outer flow. The latter is identified with a linear solution involving a lifting line, but the centerline of the planform is not required to be straight and unyawed. The existence of a similarity in the three-dimensional flow structure for a certain oblique-wing geometry is demonstrated, along with a solution to the reduced problem in a high-subcritical case.

Cheng, H. K.↗