Slender Wings Research Articles

Effect of Angle of Attack and Mach Number on Slender-Wing Unsteady Aerodynamics

An analytic theory is presented in which the classical slender wing theory is modified to account for the combined effects of large angle of attack and nonsonic Mach number on the unsteady aerodynamics. The computed results agree well with available static and dynamic experimental data for slender delta wings in the Mach number range Or^A/^ <2.8. The method was extended to compute the unsteady aerodynamics of the space shuttle orbiter by defining an equivalent slender wing using static experimental data. The results obtained in this manner are in good agreement with dynamic experimental results for the Mach number range 0.3 <M00< 0.95.

Approximate Nonlinear Slender Wing Aerodynamics

On present-day high-performance aircraft, a large portion of the lift at moderate to high angles of attack is produced by leading-edge vortices, generated by flow separation off the highly swept leading edges of the lifting surfaces employed. It has been shown in an earlier paper how the vortex effects can be superimposed on a modified slender wing theory to give the unsteady longitudinal characteristics of sharp-edged delta wings up to very high angles of attack. The present paper extends the previous analysis to include the effects of leading-edge roundness and trailing-edge sweep on the aerodynamic characteristics. The paper also derives analytic means for prediction of the yaw stability of slender wings and the first-order effects of Mach number. Universal scaling laws are defined for rapid preliminary design estimates of the slender wing lift and rolling moment.

Similarity in Vortex Asymmetries over Slender Bodies and Wings

Similarity in Vortex Asymmetries over Slender Bodies and Wings

Rudder effectiveness and course-keeping stability in shallow water: A theoretical model

This paper presents a hydrodynamic model for the rudder action of a ship in shallow water, which is based on two ideas. 1. The ship-rudder system is considered as a slender wing, and the rudder acts as a trailing-edge flap. 2. The shallow-water effec

Load distributions on slender delta wings having vortex flow

Results obtained through application of potential-flow theory based on a suction flow analogy for incompressible flow are compared to attached-flow theory and to experimental data acquired for sharp-edged delta wings. The error incurred in predicting structural loads on the basis of attached-flow theory is investigated. Force and moment coefficients and load distributions are used in the comparisons. The root bending moment can be estimated by assuming vortex lift concentrated at the wing leading edge. While this may entail some error at large angles of attack (owing to inboard movement of the center of vortex lift), it may furnish an upper bound in evaluating results based on other theories.

Spanwise cambered delta wing with leading-edge separation

Smith's method of calculating flow with leading separation on plane delta wings in subsonic flow is extended to the case of spanwise cambered delta wings, through the use of a system of conformal transformations. A numerical procedure to develop the required transformation is described. Using the transformations, a study of the effect of spanwise camber on the flow characteristics such as vortex core location and strength, sheet shape, pressure distribution, and normal force is made on a conically cambered delta wing. It is found that, at a given incidence measured from the respective zero lift angle, the core vortex on the cambered wing lies more outboard towards the leading edge and closer to the wing surface than that on the plane wing. Core and sheet vortex strengths of the cambered wing are less than those of plane wings. Significant changes in sheet shape and the location and magnitude of suction peaks are observed as a function of spanwise camber. However, with increase in incidence, the camber wing characteristics approach those of the plane wing, indicating the diminishing influence of spanwise camber on the flow details at large incidence. Since the theoretical flow model is based on the assumption of conical flow in the separated flow field and slender wing theory for attached flow, the method is applicable in the forward region near the apex of low aspect ratio wings.

Lift augmentation on a moderately swept wing by spanwise blowing

At present it is still very difficult to predict for a given incidence, sweep-angle, leading-edge shape and Reynolds Number, whether the flow around a wing will remain attached or separate either from the upper surface as a bubble or from the leading edge as a vortex sheet which rolls up above the wing. Various attempts have been made to remove this uncertainty and it was suggested by Küchemann that it should be possible to design wings which combine coiled vortex sheets, originating from the inner part of the leading edge, with attached flow over the leading edge of the outer part of the wing. In this way some of the properties of slender wings could be combined with some properties of swept wings. His original model consisted of a swept-wing planform modified by inboard leading-edge wing strakes, the purpose of the latter being to provide the inboard vortex sheets. A similar idea has now been used in the wing design of the YF-16 lightweight fighter.

Aerodynamics of slender rolling wings at incidence in separated flow

A solution to the problem of slender wings in roll about the wind axis and at angle of attack is presented. The basic approach used is a variation of that of Brown and Michael interpreted to take into account the antisymmetrical component in the resultant flow. A pressure distribution function is derived and plotted in a representative range of the key parameters, (p,a,s()) and a general expression for the evaluation of the damping contribution in roll caused by leading-edge separation in slender wings is given. The method is applied here for the evaluation of the roll damping moment and pitch coupling of a basic delta-wing, but the pressure distribution function is given in generalized form. This should enable the flow characteristics on more general rolling configurations to be reliably assessed within the limitation of the model adopted.

Supersonic Flow Past a Slender Delta Wing. An Experimental Investigation Covering the Incidence Range –5° ≤ α ≤ 50°

SummaryA detailed survey of a delta wing of 70° sweep has been performed at M = 2.5. The measurements include upper- and lower-surface pressure distributions, schlieren photographs, vapour-screen photographs and surface oil-flow visualisation. The results have been compared with thin-shock-layer theory and various other predictions.

Unsteady hypersonic flow over delta wings with detached shock waves

The problem of pitching oscillating slender delta wings with detached shock waves in hypersonic flow is studied using Messiter's thin shock-layer theory. The amplitude of oscillation is assumed small and a perturbation method is employed. Closed-form simple formulas are obtained for the unsteady pressure field and for the aerodynamic derivatives of the delta wings which are valid for general frequencies. It is found that within the thin shock-layer approximation, the slender delta wings with detached shock waves pitching in hypersonic stream are always stable dynamically. An accurate perturbation solution to Meissiter's functional-differential equation, which is required in calculating the steady and unsteady flowfields, is also obtained.

Aerodynamic characteristics of slender wings with sharp leading edges - A review

This paper presents an overview of the current state-of-the-art regarding slender wings with sharp leading edges; i.e., wings characterized by the presence of leading edge separation at most angles of attack. Several theoretical methods are discussed in detail and their results are compared with experimental data. Both steady and some unsteady flows are considered. No one theory adequately predicts all aspects of the flow process, and more work is needed, particularly in the fields of vortex control and unsteady flow.

Near-field supersonic flow pattern of slender delta wings

There is a particular need for developing analytical methods that are capable of accurately predicting the near-field flow pattern about arbitrary aircraft configuration for design optimization in connection with sonic boom as well as performance of the vehicle. Analytical studies provide a tool for understanding the near-field effects of the variations in the shape of the aircraft configuration. In the present work the theory of linearized conical flow has been applied to calculate pressure distributions over slender delta wings and at points in the field away from the wings. The present study also gives linearized results of the variations of some of the important wing parameters. Near-field flow patterns due to both first and second order conical flow fields around delta wings have been worked out. Slender delta wings with constant angle of attack, camber and thickness distribution along the span have been considered. Whitham's quasilinear approach is used for these slender delta wings to obtain a first-order uniformly valid solution. All these results are compared with those obtained from the equivalent body theory and significant differences are observed in the near-field region. Since a complete flow pattern is given the present work may be used for other aerodynamic applications.

Unsteady Aerodynamics of Slender Delta Wings at Large Angles of Attack

An analysis of the steady and unsteady aerodynamics of sharp-edged slender wings has been performed. The results show that slender wing theory can be modified to give the potential flow static and dynamic characteristics in incompressible flow. A semiempirical approximation is developed for the vortex-induced loads, and it is shown that the analytic approximation for sharp-edged slender wings gives good prediction of experimentall y determined steady and unsteady aerodynamics. The results indicate that the effects of delta planform lifting surfaces can be included in a simple manner when determining the aeroelastic characteristics of the space shuttle lift-off configuration.

Calculation of Initial Vortex Roll-Up in Aircraft Wakes

Melzig, H. D., The Dynamic Loading on Parachute Canopies, AIAA Aerodynamic Deceleration Systems Conference, AIAA, Houston, Texas, 1966. Poppleton, E. D., private communication, Univ. of Sydney, Sydney, Australia. Karmacheti, Principles of Ideal Fluid Aerodynamics, Wiley, New York, 1966. Wood, R. D., Pressure Distributions on Parachutes During Inflation, Ph.D. thesis, Univ. of Sydney, 1970. Brown, C. E. and Michael, W. H., On Slender Wings with Leading Edge Separation, TN 3430,1955, NACA. Ibrahim, S. K., Apparent Added Mass and Moment of Inertia of Cup-Shaped Bodies in Unsteady Incompressible Flow, Ph.D. thesis, University of Minnesota, 1965.

Slender Delta Wing with Conical Camber

The slenderness assumption of Munk (1924) and Jones (1946), made over and above that of linearization, has often been used to get closed form analytical solutions for wings, bodies, and their combinations. Here, simple expressions are obtained for the aerodynamic characteristics of a slender delta wing, exhibiting an even-order polynomial twist distribution in the spanwise coordinate. Carafoli (1956) derived an integral equation which relates the twist distribution to the pressure distribution. Linearized theory predicts two kinds of solution: one in which a leading edge singularity appears, and the other in which the leading edge experiences zero load.

Unsteady Transonic Flow Analysis for Low Aspect Ratio, Pointed Wings

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flowfield. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms. Input for the program includes planform shape, acceleration constant, pitch axis location, and frequency of oscillation. Sample calculations were performed for the delta, convex, and concave wings including a possible space shuttle configuration. The results were compared with those obtained by the slender body theory and by Landahl's theory. The present method obtained more negative dam ping-in-pitch than that predicted by Landahl's theory. In particular, the present method provides the stability derivatives in the low-frequency range where Landahl's theory breaks down.

Calculation of slender wing with rolling-up vortex sheet along side edges

The Report deals with a characteristic flow field around a slender rectangular thin wing, where free vortices, which separate from side edges, roll up and form a symmetrical spiral vortex sheet. The aims are to obtain lift distribution and to grasp the macroscopic flow field around the wing.Referring to the observed flow pattern around the wing by means of a hydrogen bubble method in a water tunnel, a simple flow model is assumed. The model consists of a pair of core vortices and feed vortex sheets which emerge from side edges to the core vortices.With the simplification of the flow field, boundary conditions need to be made less detailed. That is, the condition on the wing surface is satisfied only along the center line of it, and the condition for the free vortices is simplified to the condition that total forces acting on the free vortices are zero.By the method, reasonable results are obtained for normal force coefficient, center of pressure and average location of core vortices.

A Vortex Entrainment Model Applied to Slender Delta Wings

A mathematical model of the vortex flow over a slender sharp-edged delta wing is proposed, and is shown to provide good agreement with the experiment. Although the technique requires experimental data in the form of the vortex core locations, it does account for the previously ignored mass entrainment of the vortex core.

Separated Flow Past a Slender Delta Wing at Incidence

SummarySolutions to the problem of separated flow past slender delta wings for moderate values of a suitably defined incidence parameter have been calculated by Smith, using a vortex sheet model. By increasing the accuracy of the finite-difference technique, and by replacing Smith’s original nested iteration procedure, to solve the non-linear simultaneous equations that arise, by a Newton’s method, it is possible to extend the range of the incidence parameter over which solutions can be obtained. Furthermore for sufficiently small values of the incidence parameter, new and unexpected results in the form of vortex systems that originate inboard from the leading edge have been discovered. These new solutions are the only solutions, to the author’s knowledge, of a vortex sheet leaving a smooth surface.Interest has centred upon the shape of the finite vortex sheet, the position of the isolated vortex, and the lift, and variations of these quantities are shown as functions of the incidence parameter. Although no experimental evidence is available, comparisons are made with the simpler Brown and Michael model in which all the vorticity is assumed to be concentrated onto an isolated line vortex. Agreement between these two models becomes very close as the value of the incidence parameter is reduced.

Optimising the shape

THE ECONOMIC and operational efficiency of any supersonic airliner depends on the successful reconciliation of two conflicting aerodynamic requirements: good control and handling characteristics at subsonic and transonic speeds and low trim drag at supersonic speeds. Years of aerodynamic research have established the slender delta wing as the optimum shape for mach two cruise. In the Concorde design, the basic slender delta was modified by cambering the profile and tapering the forward part of it, refining the wingtips and leading edges to give improved low speed controllability without detriment to supersonic performance. Thousands of hours in different wind tunnels have enabled optimisation of the shape of the aircraft. Some results which were not available in time for incorporation on the prototypes have already been embodied on the pre‐production and production planes. Even though some of these modifications, such as elongation, redesigned nose vizor and tail shape were not applied for aerodynamic improvements, they have nevertheless affected aerodynamics.