Limitations of lifting-line theory for estimation of aileron hinge-moment characteristics
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AILERONS - HINGE MOMENTS↗
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A least-squares procedure for the solution of the lifting-line integral equation
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LIFT DISTRIBUTION, WING-SPAN↗
A modified lifting line theory for wing-propeller interference
An inviscid incompressible model for the interaction of a wing with a single propeller slipstream is presented. The model allows the perturbation quantities to be potential even though the undisturbed flow is rotational. The governing equations for the spanwise lift distribution are derived and a simple method of solving these is indicated. Spanwise lift and induced drag distribution for two cases are computed.
Prabhu, R. K.↗
Correction of the lifting-line theory for the effect of the chord
It is shown that a simple correction for the chord of a finite wing can be deduced from the three-dimensional potential flow around an elliptic plate. When this flow is compared with the flow around a section of an endless plate, it is found that the edge velocity is reduced by the factor 1/E, where E is the ratio of the semiperimeter to the span. Applying this correction to the circulation brings the theoretical lift into closer agreement with experiments.
LIFT CURVES-SLOPE↗
Results of the integration of a transonic full-potential analysis program with a free-wake lifting-line program for hovering rotors
The hovering performance predictions of the TFAR1 and OPLIN codes and the experimental data are discussed. The TFAR1 program solves the full-potential equation in a rotor-fixed coordinate system by use of the line relaxation method. The OPLIN program calculates the positions of wake vortices and rotor performance using the influence-coefficient-and-lifing-line method. The two programs are combined by adding the induced velocities from the OPLIN code to the near flow-field of the rotor from the TFAR1 code. Results show that the TFAR1 program converges better with the downwash-coupling method than the twist correction method to include the wake downwash.
Chung, Song-Young↗
Linearized lifting-surface and lifting-line evaluations of sidewash behind rolling triangular wings at supersonic speeds
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Bobbitt, Percy J↗
Summary and recent results from the NASA advanced High Speed Propeller Research Program
Advanced high-speed propellers offer large performance improvements for aircraft that cruise in the Mach 0.7 to 0.8 speed regime. The current status of the NASA research program on high-speed propeller aerodynamics, acoustics, and aeroelastics is described. Recent wind tunnel results for five 8- to 10-blade advanced models are compared with analytical predictions. Test results show that blade sweep was important in achieving net efficiencies near 80 percent at Mach 0.8 and reducing near-field cruise noise by dB. Lifting line and lifting surface aerodynamic analysis codes are under development and some initial lifting line results are compared with propeller force and probe data. Some initial laser velocimeter measurements of the flow field velocities of an 8-bladed 45 deg swept propeller are shown. Experimental aeroelastic results indicate that cascade effects and blade sweep strongly affect propeller aeroelastic characteristics. Comparisons of propeller near-field noise data with linear acoustic theory indicate that the theory adequate predicts near-field noise for subsonic tip speeds but overpredicts the noise for supersonic tip speeds. Potential large gains in propeller efficiency of 7 to 11 percent at Mach 0.8 may be possible with advanced counter-rotation propellers.
Mitchell, G. A.↗
Lift and Drag of Wings with Small Span
The lift coefficient of!a wing of small span at first shows a linear increase for the increasing angle of attack, but to a lesser degree then was to be expected according to the theory of the lifting line; thereafter the lift coefficient increases more rapidly than linearity, as contrasted with the the theory of the lifting line. The induced drag coefficient for a given lift coefficient, on the other hand, is obviously much smaller than it would be according to the theory. A mall change in the theory of the lifting line will cover these deviations.
Weinig, F.↗
Line-vortex theory for calculation of supersonic downwash
The perturbation field induced by a line vortex in a supersonic stream and the downwash behind a supersonic lifting surface are examined to establish approximate methods for determining the downwash behind supersonic wings. Lifting-lines methods are presented for calculating supersonic downwash. A bent lifting-line method is proposed for computing the downwash field behind swept wings. When applied to triangular wings with subsonic leading edges, this method gives results that, in general, are in good agreement with the exact linearized solution. An unbent lifting-line method (horseshoe-vortex system) is proposed for unswept wings. This method is applied to determine downwash behind rectangular wings with aspect ratios of 2 and 4. Excellent agreement with exact linearized theory is obtained for both aspect ratios by placing the lifting line at the 1/2-chord point. The use of lifting-lines therefore appears promising for obtaining estimates of the downwash behind supersonic wings.
Mirels, Harold↗
Wake model for helicopter rotors in high speed flight
Two alternative approaches are developed to calculate blade-vortex interaction airloads on helicopter rotors: second order lifting-line theory, and a lifting surface theory correction. The common approach of using a larger vortex core radius to account for lifting-surface effects is quantified. The second order lifting-line theory also improves the modeling of yawed flow and swept tips. Calculated results are compared with wind tunnel measurements of lateral flapping, and with flight test measurements of blade section lift on SA349/2 and H-34 helicopter rotors. The tip vortex core radius required for good correlation with the flight test data is about 20 percent chord, which is within the range of measured viscous core sizes for helicopter rotors.
Johnson, Wayne R.↗
Application of theory to propeller design
The various theories concerning propeller design are discussed. The use of digital computers to obtain specific blade shapes to meet appropriate flow conditions is emphasized. The development of lifting-line and lifting surface configurations is analyzed. Ship propulsive performance and basic propeller design considerations are investigated. The characteristics of supercavitating propellers are compared with those of subcavitating propellers.
Cox, G. G.↗
New test techniques and analytical procedures for understanding the behavior of advanced propellers
Analytical procedures and experimental techniques were developed to improve the capability to design advanced high speed propellers. Some results from the propeller lifting line and lifting surface aerodynamic analysis codes are compared with propeller force data, probe data and laser velocimeter data. In general, the code comparisons with data indicate good qualitative agreement. A rotating propeller force balance demonstrated good accuracy and reduced test time by 50 percent. Results from three propeller flow visualization techniques are shown which illustrate some of the physical phenomena occurring on these propellers.
Stefko, G. L.↗
Summary of recent NASA propeller research
Advanced high-speed propellers offer large performance improvements for aircraft that cruise in the Mach 0.7 to 0.8 speed regime. At these speeds, studies indicate that there is a 15 to near 40 percent block fuel savings and associated operating cost benefits for advanced turboprops compared to equivalent technology turbofan powered aircraft. Recent wind tunnel results for five eight to ten blade advanced models are compared with analytical predictions. Test results show that blade sweep was important in achieving net efficiencies near 80 percent at Mach 0.8 and reducing nearfield cruise noise by about 6 dB. Lifting line and lifting surface aerodynamic analysis codes are under development and some results are compared with propeller force and probe data. Also, analytical predictions are compared with some initial laser velocimeter measurements of the flow field velocities of an eightbladed 45 swept propeller. Experimental aeroelastic results indicate that cascade effects and blade sweep strongly affect propeller aeroelastic characteristics. Comparisons of propeller near-field noise data with linear acoustic theory indicate that the theory adequately predicts near-field noise for subsonic tip speeds but overpredicts the noise for supersonic tip speeds.
Mikkelson, D. C.↗
Summary of recent NASA propeller research
Advanced high speed propellers offer large performance improvements for aircraft that cruise in the Mach 0.7 to 0.8 speed regime. At these speeds, studies indicate that there is a 15 to near 40 percent block fuel savings and associated operating cost benefits for advanced turboprops compared to equivalent technology turbofan powered aircraft. Recent wind tunnel results for five eight to ten blade advanced models are compared with analytical predictions. Test results show that blade sweep was important in achieving net efficiencies near 80 percent at Mach 0.8 and reducing nearfield cruise noise about 6 dB. Lifting line and lifting surface aerodynamic analysis codes are under development and some results are compared with propeller force and probe data. Also, analytical predictions are compared with some initial laser velocimeter measurements of the flow field velocities of an eight bladed 45 swept propeller. Experimental aeroelastic results indicate that cascade effects and blade sweep strongly affect propeller aeroelastic characteristics. Comparisons of propeller nearfield noise data with linear acoustic theory indicate that the theory adequately predicts nearfield noise for subsonic tip speeds, but overpredicts the noise for supersonic tip speeds.
Mikkelson, D. C.↗
Flow phenomena on plates and airfoils of short span
Investigations on the flow phenomena at plates and cambered models were carried out with the aid of force measurements, some pressure distribution measurements, and photographic observation. The experimental methods are described and the results given. Section III of this work gives a comprehensive account of the results and enables us to see how nearly the lift line and lift surface theories agree with the experimental results.
Winter, H↗
Use of HART-II Measured Motion in CFD
This presentation examines the use of HART-II measured rotor blade motion in computational fluid dynamics (CFD). Historically, comprehensive analyses were used for input to acoustic calculations. These analyses focused on lifting line aerodynamics and beam models. However, there is a a need to evolve lifting line aerodynamics to first principles, notably the use of CFD instead of lifting line. The current analysis focuses on CFD and computational structural dynamics (CSD) coupling. Beam models are still very good (CSD is typically from comprehensive analysis), but generally CFD replaced aerodynamics in comprehensive analysis. This presentation examines both CFD and CSD individually and includes predictions using measured motion as well as predictions using measured motion versus coupled motion and calculations of "correct" airloads, noise and vibration.
Boyd, D. Douglas, Jr.↗
Calculation of blade-vortex interaction airloads on helicopter rotors
Two alternative approaches area developed to calculate blade-vortex interaction airloads on helicopter rotors, second-order lifting-line theory and a lifting-surface theory correction. The common approach of using a larger vortex core radius to account for lifting-surface effects is quantified. The second-order lifting-line theory also improves the modeling of low aspect-ratio blades yawed flow, and swept tips. Calculated results are compared with wind-tunnel measurements of lateral flapping, and with flight test measurements of blade section lift on SA349/2 and H-34 helicopter rotors. The tip vortex core radius required for good correlation with the flight test data is about a 20-percent chord, which is within the range of measured viscous core sizes for helicopter rotors.
Johnson, Wayne↗
On the general theory of thin airfoils for nonuniform motion
General thin-airfoil theory for a compressible fluid is formulated as boundary problem for the velocity potential, without recourse to the theory of vortex motion. On the basis of this formulation the integral equation of lifting-surface theory for an incompressible fluid is derived with the chordwise component of the fluid velocity at the airfoil as the function to be determined. It is shown how by integration by parts this integral equation can be transformed into the Biot-Savart theorem. A clarification is gained regarding the use of principal value definitions for the integral which occur. The integral equation of lifting-surface theory is used a s the starting point for the establishment of a theory for the nonstationary airfoil which is a generalization of lifting-line theory for the stationary airfoil and which might be called "lifting-strip" theory. Explicit expressions are given for section lift and section moment in terms of the circulation function, which for any given wing deflection is to be determined from an integral equation which is of the type of the equation of lifting-line theory. The results obtained are for airfoils of uniform chord. They can be extended to tapered airfoils. One of the main uses of the results should be that they furnish a practical means for the analysis of the aerodynamic span effect in the problem of wing flutter. The range of applicability of "lifting-strip" theory is the same as that of lifting-line theory so that its results may be applied to airfoils with aspect ratios as low as three.
BIBLIOGRAPHY-WINGS↗