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A wind-tunnel investigation has been performed to quantify the effects of a jet on the leading-edge vortices generated by a 70-deg-sweep sharp-edged delta wing at low Reynolds numbers. Efforts were made ot optimize the jet nozzle position with respect to maximum lift increments. Both half-span force-balance testing and half- and full-span flow visualization tests were conducted. Two angles of attack were investigated, 30 and 35 deg, at Reynolds numbers of 150,000 and 200,000. Aerodynamic enhancement, including lift and drag gains of about 20 and 17 percent respectively, were measured. Results indicate an optimum jet nozzle location to be close to the leading edge, tangent to the upper wing surface, and in a direction aligned parallel to the leading edge. Nozzle interference effects, especially near the apex, were not negligible.

Various existing unsteady aerodynamic strip theories which have been developed in the past for both fixed and rotary wing aeroelastic analyses are modified in the paper so as to make them applicable to the coupled flap-lag-torsional aeroelastic problem of a rotor blade in hover. These corrections are primarily due to constant angle of attack, constant inflow and variable free stream velocity due to lead-lag motion. Next, the modified strip theories are incorporated in a coupled flap-lag-torsional aeroelastic analysis of the rotor blade in hover and the sensitivity of the aeroelastic stability boundaries to the aerodynamic assumptions is examined.

Recent wind tunnel studies have shown that significant improvements in wing efficiency and climb performance can be achieved using wing extensions having sharp edges and unmodified upper airfoil contours. Based on tests of six configurations, a simple tip shape provided the best wing efficiency at high lift conditions without penalty during cruise conditions. The best configuration tested exhibited more than 20 percent improvement in the maximum rate of climb, plus a reduction in stall speed and a slight improvement in cruise performance over a baseline tip with a round edge. In addition to measurements that were used to determine performance, flow visualization studies provided insight into reasons for improved wing efficiency. Tests were conducted using a high performance general aviation aircraft model with a tapered, cantilevered wing.

A Preliminary Design Study of large turbulent flow military transport aircraft has been made. The study airplanes were designed to carry a heavy payload (350,000 lb) for a long range (10,000 nmi). The study tasks included: Wing geometry/cruise speed optimization of a large cantilever wing military transport airplane; Preliminary design and performance evaluation of a strut-braced wing transport airplane; and Structural analyses of large-span cantilever and strut-braced wings of graphite/epoxy sandwich construction (1985 technology). The best cantilever wing planform for minimum takeoff gross weight, and minimum fuel requirements, as determined using statistical weight evaluations, has a high aspect ratio, low sweep, low thickness/chord ratio, and a cruise Mach number of 0.76. A near optimum wing planform with greater speed capability (M = 0.78) has an aspect ratio = 12, quarter chord sweep = 20 deg, and thickness/chord ratio of 0.14/0.08 (inboard/outboard).

An investigation has been conducted in the NASA Langley Research Center's 30- by 60-Foot Wind Tunnel on a full-scale semispan model to evaluate and document the low-speed, high-lift characteristics of a business-jet class wing utilizing the HSNLF(1)-0213 airfoil section and a single slotted flap system. In addition to the high-lift studies, evaluations of boundary layer transition effects, the effectiveness of a segmented leading-edge droop for improved stall/spin resistance, and roll control effectiveness with and without flap deflection were made. The wind-tunnel investigation showed that deployment of a single-slotted trailing-edge flap provided substantial increments in lift. Fixed transition studies indicated no adverse effects on lift and pitching-moment characteristics for either the cruise or landing configuration. Subscale roll damping tests also indicated that stall/spin resistance could be enhanced through the use of a properly designed leading-edge droop.

The flow over the B-1 wing is studied computationally, including the aeroelastic response of the wing. Computed results are compared with results from wind tunnel and flight tests for both low- and high-sweep cases, at 25.0 and 67.5 deg, respectively, for selected transonic Mach numbers. The aerodynamic and aeroelastic computations are made by using the transonic unsteady code ATRAN3S. Steady aerodynamic computations compare well with wind tunnel results for the 25.0 deg sweep case and also for small angles of attack at 67.5 deg sweep case. The aeroelastic response results show that the wing is stable at the low-sweep angle for the calculation at the Mach number at which there is a shock wave. In the higher-sweep case, for the higher angle of attack at which oscillations were observed in the flight and wind tunnel tests, the calculations do not show any shock waves. Their absence lends support to the hypothesis that the observed oscillations are due to the presence of leading-edge separation vortices and not to shock wave motion, as was previously proposed.

This technical note summarizes experimental lifting-surface wake data taken from a 1/10-scale, reflection-plane a model of the X-29 Forward Swept Wing Demonstrator. The model is configured with and without the canard to illustrate the canard/wing wake interactions. The data collected comprises total, dynamic, and static pressures as well as local velocity magnitudes and directions for a series of points around this model. The data point are arrayed to include flow regions near the model as well as the freestream wake regions downstream of its canard and wing.

Composite material aeroelastic tailoring is presently explored as a means for the correction of the roll trim imbalance of oblique-wing aircraft configurations. The concept is demonstrated through the analysis of a realistic oblique wing by a static aeroelastic computational procedure encompassing the full potential transonic aerodynamic code FLO22 and a Ritz structural plate program that models the stiffness due to symmetrical-but-unbalanced composite wing skins. Results indicate that asymetric composite tailoring reduces the aileron deflection needed for roll equilibrium, and reduces control surface hinge moment and drag. Wing skin stresses are, however, very high.

An experimental wind-tunnel study to determine the divergence characteristics of a high-aspect ratio, forward-swept wing has been conducted in the NASA Langley Research Center (LaRC) Transonic Dynamics Tunnel (TDT). The rectangular wing used for this study had a panel aspect ratio of 9.16 (lambda = 0 deg.) and the sweep angle could be set at lambda = 0 deg., -15 deg., -30 deg., -45 deg., or -60 deg. A rectangular wing tip shape was tested at each of these sweep angles. In addition, a tip shape parallel to the freestream flow was tested for a wing sweep angle of lambda = -45 deg. The root of the wing was cantilever mounted to the wall of the wind tunnel. Divergence conditions were measured at M = 0.4 for each sweep angle and tip configuration tested. Subcritical response techniques were used to extrapolate to the divergence conditions during the wind-tunnel test. The primary objective of this test was to obtain data which could be used to verify for this configuration the divergence prediction capability of an aeroelastic analysis code. Subsonic lifting surface theory (kernel function) aerodynamics are utilized by this particular code. The analytical predictions of divergence were found to be significantly conservative at all forward sweep angles. At lambda = -45 deg., the analysis was 14 percent conservative. The effect of the two tip shapes on the divergence dynamic pressure was predicted accurately by the analysis. The divergence condition for the tip shape parallel to the flow occurred at a dynamic pressure 14 percent higher than the divergence condition with a rectangular tip shape.

Pressure data measured on the flexible DAST ARW-2 wing are compared with results calculated using the transonic small perturbation code XTRAN3S. A brief description of the analysis is given and a recently-developed grid coordinate transformation is described. Calculations are presented for the rigid and flexible wing for Mach numbers from 0.60 to 0.90 and dynamic pressures from 0 to 1000 psf. Calculated and measured static pressures and wing deflections are compared, and calculated static aeroelastic trends are given. Attempts to calculate the transonic instability boundary of the wing are described.

Pressures were measured with Freon as the test medium. Data taken at M = 0.9 is presented for static and oscillatory deflections of the trailing edge control surface and for the wing in pitch. Comparisons of the static measured data are made with results computed using the Bailey-Ballhaus small disturbance code.

Low-speed wind-tunnel tests were performed on a generic forward-swept-wing aircraft model in the 7- by 10-Foot Wind Tunnel (No. 2) at Ames Research Center. The effects of various configurational changes and control-surface deflections on the performance of the model were measured. Six-component force measurements were augmented by flow-visualization photographs, using both surface oil-flow and tufts. It was found that the tendency toward premature root separation on the forward-swept wing could be reduced by use of either canards or leading-edge wing strakes and that differential canard deflections can be used to produce a direct side-force control.

Nonlinear unsteady aerodynamic loads on rectangular and delta wings in an incompressible flow are calculated by using an unsteady vortex-lattice model. Examples include flows past fixed wings in unsteady uniform streams and flows past wings undergoing unsteady motions. The unsteadiness may be due to gusty winds or pitching oscillations. The present technique establishes a reliable approach which can be utilized in the analysis of problems associated with the dynamics and aeroelasticity of wings within a wide range of angles of attack.

A series of low-speed wind tunnel tests on a 70-degree sharp leading-edged delta wing at both static and dynamic conditions were performed to investigate the aerodynamic forces and moments. Forces and moments were obtained from a six component internal strain gauge balance. Static results compared well with the previous experimental findings. Large amplitude dynamic motion was produced by sinusoidally oscillating the model over a range of reduced frequencies. Substantial force and moment overshoots, a delay in dynamic stall, and hysteresis loops between the values of aerodynamnic loads in upstroke and downstroke motion were observed, all of which were strong functions of the reduced frequency. The aerodynamic forces and moments were influenced by the Reynolds number. Asymmetrical vortex bursting produced by nonzero sideslip angle created a complex rolling moment variations with angle of attack.

Flight-derived aerodynamic heat-transfer data for the orbiter wing lower surface, from STS-2, -3, and -5, are presented and compared with both ground-based experimental results and state-of-the-art computational flowfield results for a nominal angle of attack of 40 degrees. The flight data clearly show the development of the interference heat-transfer region on the wing lower surface resulting from the downstream effects of the bow-shock/wing-shock interaction. The location of the interference heating region is well correlated with a region of minimum static enthalpy near the boundary-layer edge as predicted by a 3-dimensional, inviscid flowfield computation. The magnitude of the interference heat transfer is no greater than the undisturbed laminar heat transfer which occurs during the 'peak aerodynamic heating' portion of entry.

Aerodynamical closely coupled dual wing configurations of unequal chords are investigated for medium speed general aviation applications. Vortex panel and momentum boundary layer analysis are utilized for the two-dimensional predictions. A multi-surface vortex lattice method is used for the three-dimensional predictions. In the process of searching for the highest lift to drag ratio upper airfoil to lower airfoil chord ratios, both greater than and less than one, are investigated in terms of stagger, decalage angle, and gap. With the optimum chord ratio, at the optimum stagger and gap, proper spanwise decalage distribution is shown to yield the lowest two dimensional drag results. Various wing taper ratios and wing twists are investigated to increase wing efficiency. Comparisons are made between optimized dual and optimized single wing configurations both with the same fuselage, stabilator surfaces, engines, payload, and fuel. The dual wing configuration is shown to have significantly less drag and hence longer range than the conventional single wing configuration.

A study has been conducted to explore the use of existing aerodynamic techniques to design a new supersonic cruise wing for an existing fighter wind-tunnel model. In addition to the usual wing design constraints of lift, pitching moment, and minimum drag, a ground rule was imposed that the wing had to fit on the existing fuselage. Experimental wind-tunnel results were obtained for a camber design and a reference flat wing. The flat wing was also fitted with leading-edge flaps which approximate the cruise camber design. The experimental results indicate that significant improvements in supersonic cruise capability can be obtained by a new wing designed using existing supersonic aerodynamic techniques.

The problem of estimating the aerodynamic characteristics of a wing body configuration of a spinning airplane at extreme angles of attack and spin rates is approached by the application of strip theory. Semiempirical methods are used to estimate the aerodynamic force distributions over each component using static, nonrotational wind-tunnel test data. To these predictions, corrections are applied to account for the primary rotational flow effects which are significant at large spin rates. The results of this modified strip theory are shown to be in good agreement with spin tunnel rotary balance test data.

The feasibility of controlling vortex interactions or merger on a blended chine forebody and delta wing configuration was experimentally investigated. Low-speed wind tunnel diagnostics using smoke visualizations and wing upper-surface pressure measurements were performed on a generic 60 deg delta and chine forebody model, to assess chine modifications and leading edge flaps. Both techniques were shown to promote uncoupled vortex flows at high angles of attack and sideslip, with significant influence on the wing flow field, indicating potential for alleviating adverse high-alpha characteristics of blended chine swept wing configurations.

A wing designed using the concept of attached supercritical crossflow for supersonic maneuvering aircraft wings has been built and tested. The detailed wing shape was determined using nonlinear potential flow computational aerodynamics methods to obtain a specified target pressure distribution. The test results showed that the target pressures were essentially obtained and that the drag-due-to-lift values at maneuver lift coefficients were considerably less than those expected using linear theory design procedures. The paper provides a detailed description of the wing design and test, and an analysis of the results.

A three-dimensional Euler aerodynamic method (TEAM) is used to simulate the interaction of free vortices with lifting surfaces. The free vortices considered here arise from flow separation along sharp leading edges of slender swept wings at moderate-to-high angles of attack and shed in the wake behind lifting wings. Computed results for a 74 deg delta wing, a 75/62 deg double-delta wing body, and a canard-wing-body configuration are correlated with experimental data to evaluate TEAM's capabilities

The present work presents results from two research studies that provide information on the fluctuating pressures generated by the use of powered-lift systems in STOL aircraft. Data are given for several chordwise and spanwise locations on large-scale models of an externally blown flap (EBF) configuration and an upper surface blown flap (USB) configuration in which actual jet engines were used. Pressure levels were high enough to indicate that special design effort will be required to avoid acoustic fatigue failures of wing and flap sturctures. The observation that pressure levels did not decrease very much with increased distance from the engine exhaust center line suggests that a STOL aircraft fuselage, which is in relatively close proximity to the engines for aerodynamic reasons, will be subjected to unusually high external overall fluctuating pressure levels (OAFPLs) that may cause difficulty in control of the cabin noise level.

A procedure is presented for determining the optimal cover panel thickness of a wing structure to meet specified strength and static aeroelastic divergence requirements for minimum weight. Efficient reanalysis techniques using discrete structural and aerodynamic methods are used in conjunction with redesign algorithms driven by optimality criteria. The optimality conditions for the divergence constraint are established, and expressions are obtained for derivatives of the dynamic pressure at divergence with respect to design variables. The procedure is applied to an oblique wing aircraft where strength and stiffness are critical design considerations for sizing the cover thickness of the wing structure.

Data obtained through very high angles of attack from a large-scale, subsonic wind-tunnel test of a close-coupled canard-delta-wing fighter model are analyzed. The canard delays wing leading-edge vortex breakdown, even for angles of attack at which the canard is completely stalled. A vortex-lattice method was applied which gave good predictions of lift and pitching moment up to an angle of attack of about 20 deg, where vortex-breakdown effects on performance become significant. Pitch-control inputs generally retain full effectiveness up to the angle of attack of maximum lift, beyond which, effectiveness drops off rapidly. A high-angle-of-attack prediction method gives good estimates of lift and drag for the completely stalled aircraft. Roll asymmetry observed at zero sideslip is apparently caused by an asymmetry in the model support structure.

A semispan research model with a 2-ft span wing was used to measure the high lift capabilities of low aspect ratio wings utilizing powered-lift concepts. The concepts evaluated were the Circulation Control Wing (CCW), the Upper Surface Blowing (USB), and unique combination of the two (CCW/USB). Wing tip sails were used as a means of increasing the effective aspect ratio of these wings during high lift. The highest lift was generated with the CCW/USB configuration where the CCW is used as a thrust vectoring device and successfully turns the engine exhaust up to 165 deg. The lift augmentation resulting from the CCW and the turning exhaust flow produced a maximum circulation lift of 5.1 with an aspect ratio 4 wing. It is shown that this nearly approaches the theoretical maximum circulation lift (independent of the thrust contribution to lift) that can be developed for a given aspect ratio wing. The wing tip sails are effective in reducing the induced drag of these powered-lift low aspect ratio wings under high-lift conditions. The induced drag factor is reduced in some instances by 30 to 35 percent. The relatively low drag of this configuration shows that with correct operational procedure the potential for short takeoff and landing is significant.

A numerical analysis has been conducted with the three-dimensional panel code VSAERO for two interacting lifting surfaces that are separated in the spanwise direction by a narrow gap, with the angle of attack of the outboard section being set independently of the inboard section, as in the 'free tip' rotor blade system proposed for helicopters. Computed values of tip surface lift and pitching moment coefficients are correlated with experimental data to determine the most suitable method for modeling the gap region between the surfaces. It is shown that the induced drag of the tip surface is reduced for negative incidence angles relative to the inboard section.

A program of airload measurements on a family of low-aspect-ratio delta wings with sharp leading edges, subjected to large amplitude pitch transients with angles of attack up to 90 deg, is reviewed. Even for small values of the pitch-rate parameter, representative of maneuvers anticipated for agile aircraft, the force and moment overshoots can exceed by 50 percent their steady-state values. This is explained in terms of the hysteretic behavior of the breakdown locations of leading-edge vortices. An approximate theoretical model is proposed which includes the breakdown hysteresis as part of a three-term representation of the unsteady chordwise load distribution.

Wind tunnel tests were conducted on a 60 deg delta wing with three vortex flap designs to determine pressure distributions over the wing and flap. The results showed that an optimum vortex flap design depends on proper definition of the vortex flap deflection angle. They also revealed that flap thickness plays an important role in the behavior of the vortex flow over the flap and wing and can have a substantial effect on wing and flap pressure loading. Design codes which fail to account for thickness may result in a much less than optimum flap and deprive the designer of an important tool in designing an effective flap with optimum loading.

The NASA Langley Research Center has initiated a broad general aviation stall/spin research program. A rotary balance system was developed to support this effort. Located in the Langley spin tunnel, this system makes it possible to identify an airplane's aerodynamic characteristics in a rotational flow environment, and thereby permits prediction of spins. This paper presents a brief description of the experimental set-up, testing technique, five model programs conducted to date, and an overview of the rotary balance results and their correlation with spin tunnel free-spinning model results. It is shown, for example, that there is a large, nonlinear dependency of the aerodynamic moments on rotational rate and that these moments are pronouncedly configuration-dependent. Fuselage shape, horizontal tail and, in some instances, wing location are shown to appreciably influence the yawing moment characteristics above an angle of attack of 45 deg.

An experimental study of the fluctuating pressure field of a high-aspect-ratio swept transport-type wing model in transonic buffeting flow is examined. A high degree of similarity between the buffet-related features of the wing flowfield and 2-D transonic flowfields is indicated. At several spanwise stations, unsteady lift produced by the pressure fluctuations is evaluated and found to increase in intensity as local flow separation develops. Results show that although the wing does vibrate, the measured lift fluctuations are driving, and not driven by wing vibrations. The influence of tunnel-flow unsteadiness on the data is considered.

A small canard wing was installed in front of a delta wing which was mounted on a free-to-roll sting balance in a low-speed wind tunnel. The leading edge vortices, originating from the canard, enhanced self-induced roll oscillations at test conditions for which the basic delta wing would otherwise have been stable. Time-dependent roll angle, and normal and side force data recorded during these oscillations are presented along with their phase relations. It was found that the canard increased the range of angle of attack at which self-induced oscillations occurred. Also, at an angle of attack of about 46 deg asymmetric oscillations are observed.

An experimental investigation was conducted in the Langley high-speed 7- by 10-foot wind tunnel to determine the aerodynamic performance of suction applied near the wing tips above the trailing edge of a 60 deg swept Gothic wing. Moveable suction inlets were symmetrically mounted in the proximity of the trailing edge, and the amount of suction was varied to maximize wing lift. Tests were conducted at Mach 0.15, 0.30, and 0.45, and the angle of attack was varied from -4 to 50 deg. The suction augmentation increases the lift coefficient over the entire range of angle of attack. The lift improvement exceeds the unaugmented wing lift by over 20%. Moreover, the augmented lift exceeds the lift predicted by vortex lattice theory to 30 deg angle of attack. Suction augmentation is postulated to strengthen the vortex system by increasing its velocity and making it more concentrated. This causes the vortex breakdown to be delayed to a higher angle of attack

An analytical investigation of the stability and performance of a Boeing-Vertol H-21 tandem rotor helicopter equipped with floating wing fuel cells as a means of ferry range extension is described. The stability of the total system was studied with the wing located forward and directly under the helicopter center-of-gravity (cg). Two methods of stabilizing the wing oscillations about the hinge were studied: (a) A skewed hinge line, introducing a change in angle of attack as a function of the flapping disturbance; and (b) a geared trailing edge flap, mechanically linked to deflect when the wing flaps. Satisfactory stability was obtained with the wing positioned directly beneath the helicopter cg, using an unskewed hinge line, and geared flaps. The forward wing location was unsatisfactory from the standpoint of longitudinal stability for the light wing case. Flight simulator studies emphasize the need for additional lateral control to supplement that produced by the basic aircraft.

Static-force and pressure tests were conducted in the 40-in. supersonic tunnel of the von Karman Gas Dynamics Facility on a 70-deg, blunt leading-edge, semi-span delta wing. The wing consisted of three sections, triangular forward and tip panels and a rectangular main panel. Tests were made with the forward panel deflected -2.5 deg and undeflected (flat wing). Force data on the total wing and pressure data on the tip panel were obtained at Mach number 6. The angle-of-attack range was from -4 to 10 deg, and Reynolds number, based on the wing root chord, ranged from 9 x 10 to the 6th power at Mach number 3 to 18 x 10 to the 6th power at Mach number 6. Wing lift-to-drag ratio and tip panel pressure data are presented for the wing with the forward panel deflected and undeflected.

This chapter focuses on the lift and moment characteristics of an airplane. A study of wings always starts with a two-dimensional, or infinite aspect ratio, case where all sections are identical. The lift on a wing is usually described by the distribution over its surface of the aerodynamic loading. The loading, or load per unit area, is the difference between upper and lower surface pressures at a point in the plan view. For stability and control estimates, two features are of interest: (1) the total load and (2) its distribution, which determines the moment. In the range of high aspect ratio, the Prandtl lifting-line theory suffices pretty well to calculate the distribution of lift along the span. The effects of camber and twist are felt as changes in the angle of attack for zero lift, and in the aerodynamic center pitching moment as a result of the basic lift distribution. The normal force, or lift, acting on slender, axially symmetric bodies at an angle of attack are, according to the so-called slender-body theory, distributed along the body in accordance. The slender wing theory is an extension of the slender body theory, wherein the leading edge of the wing defines the diameter variation of an equivalent circular body.

Wing-body combinations analysis and design at supersonic and subsonic speeds by aerodynamic influence coefficients method

A preliminary design study of a hot cycle rotor/wing composite research aircraft is described. The hot cycle rotor/wing uses a single lightweight lifting surface which functions as both a rotor for takeoff and a fixed wing for horizontal flight. The rotary/wing is essentially an equilateral delta wing with short feathering blades at the three corners. The rotor is powered by a tip-jet hot cycle drive, and the turbojet exhaust is diverted from the rotor to provide forward propulsion. The hot cycle rotor/wing provides the advantages of hovering efficiency, low downwash velocity, and helicopter-like flying qualities for vertical and low-speed flight, in addition to the high- speed capability and cruise efficiency of the jet airplane. Its simplicity and light weight are made possible through the combined use of the all-pneumatic hot cycle drive system and the dual-purpose rotor/wing lift system. This eliminates the need for heavy and complex mechanical drive components and anti-torque tail rotor; it permits flight as a helicopter and as an airplane without recourse to duplicate lifting systems or to folding, tilting, or retracting of lift systems to effect conversion.

Developed in this report are expressions for the lift, pitching moment, and location of the aerodynamic center due to free-stream angle of attack for an isolated cylindrical wing based on a solution of Weissinger's general boundary condition for ring wings. From the components of ring vorticity expanded in a Birnbaum series and satisfying the velocity boundary-flow condition, and from the Kutta-Joukowski relation for the force on a vortex surface, the lift, moment, and aerodynamic center can be expressed in terms of the Birnbaum coefficients. It was found that the lift and pitching moments for cylindrical ring wings are substantially different from the results for two- dimensional flat plate (thin) airfoils. Calculations show a significant shift in the aerodynamic center upstream of the 1/4-chord point for cylindrical ring wings.

It is known that linearized theory predicts very low values of drag due to lift at supersonic speeds when proper planform and load distribution are used. Attempts to obtain these predicted values experimentally have met with very limited success. The failure of the linearized theory is shown to result from the attainment of a supercritical flow over the wings, an effect which is beyond the scope of simple first-order theory. By consideration of second-order terms in the pressure equation, analysis indicates that it is extremely difficult to design a cambered and twisted sweptback wing that would avoid supercritical flow at realistic lift coefficients. Nevertheless, a series of sweptback wings has been designed and tested in order to verify the analysis, and results of this investigation are described. Other approaches to the problem involve the use of supersonic edged wings preceded by fuselage-like lifting bodies. An analysis of such configurations is presented including the development of a new method for calculating optimized loadings on wings of arbitrary planform. It is shown to be necessary to account for combined lifting and volume effects in the design of such configurations.

The effect of wing tip droop on the structure and position of its trailing vortex is studied. Spanwise load distributions determined by vortex lattice theory show that the stronger vortex moves from the tip of the wing to the hinge of the drooped tip as the droop angle increases. Experimental results on model wings are given which present the strength and the induced velocity profiles of the rolled-up vortex as a function of tip geometry. These results confirm at least qualitatively, the analytical prediction. It is concluded that a droop angle of approximately 90° is optimum and results in a maximum induced velocity which is half of that produced by a plane wing.

The cited references pertain primarily to the following aerodynamic information on ring wings, also known as annular wings or circular wings: Calculation of circumferential velocity and pressure distribution, studies on flow separation phenomena at the wing leading and trailing edges, measurement of lift, drag and pitching moment, application of linearized theory to subsonic and supersonic gas flow, theory and measurement of vortex drag, measurement of three-dimensional turbulent boundary layer, determination of flutter using linearized equations, theory of stationary, inviscid, incompressible flow around the wing, studies on drag reduction, studies on interference effects of an axisymmetric fuselage or a structure on wing pressure distributions, wind tunnel tests of wings with and without a fuselage, and determination of optimum shape.

Wind tunnel tests were conducted on low aspect ratio wings in order to: (1.) Measure the oscillatory aerodynamic lift forces, pitching moments, and hinge moments acting on rectangular wings of aspect ratio 1 and 2, due to the harmonic vibration of flap or tab; (2.) Measure similar data due to static deflection of flap or tab; (3.) Measure wing pitching moment and flap hinge moment of the finite wings under zero lift conditions; and (4.) Compare these measured data with existing low aspect ratio theory.