AN INTEGRAL EQUATION RELATING THE GENERAL TIME-DEPENDENT LIFT AND DOWNWASH DISTRIBUTIONS OF FINITE WINGS IN SUBSONIC FLOW
Integral equation relating general time-dependent lift & downwash distributions of finite wings in subsonic flow
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Integral equation relating general time-dependent lift & downwash distributions of finite wings in subsonic flow
Ground erosion due to vtol downwash
Jet wake degradation and thrust characteristics of exhaust nozzles designed for VTOL downwash suppression and fuselage and ground effects
Exhaust nozzle testing using cold air flow to find effect of exit design on thrust & jet wake dynamic pressure for use in vtol downwash suppression
Wind tunnel tests of downwash aerodynamic surface incidence angles on Saturn S-1C booster coupled to Grumman C-4 orbiter shuttle
The application of the downwash-velocity potential method to the case of oscillating surfaces is developed, and calculated forces are given on rectangular airfoils of aspect ratio two rotating about midchord in subsonic flows. These are compared with other results published in the literature for reduced frequencies up to nine-tenths, and for Mach numbers up to nine-tenths. The concept of 'aerodynamic elements' is presented, the computed results representing three possible types of rectangular element.
The method of computing the Whitham F function using distributions of downwash and sidewash angles was evaluated with two different models. F functions which were calculated for a half angle cone cylinder at M infinites = 2.01, using theoretically and experimentally derived flow angles, show that the method is sensitive to small inaccuracies in the measured flow angles. An oblique wing transport model was tested at 0 deg angle of attack at M infinitely = 2.01. In this test, two different probes were used at two different distances from the model. The pressure signature derived from the F function was extrapolated and compared to the pressure signature measured at the distance of 0.87 body lengths with the static pressure probe. The agreement between the two pressure signatures was poor due to the many inaccuracies involved in using a probe designed to measure flow angularity.
This paper investigates the relative importance of including unsteady effects in the lift and downwash in the longitudinal dynamics and parameter extraction algorithm. A simple vortex system has been used to model unsteady aerodynamic effects into the longitudinal equations of motion of an aircraft. Computer-generated data and flight data were used to demonstrate that inclusion of unsteady aerodynamics in the parameter-extraction algorithm produced aerodynamic parameters that were different from those extracted when unsteady aerodynamics were left out of the algorithm. The differences between derivatives associated with the two extraction algorithms (with and without unsteady aerodynamics) were related to acceleration derivatives which usually cannot be extracted individually.
For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.
The results of an experimental investigation of the downwash and sidewash flow angles in a transverse plane behind a cruciform-wing and body combination are presented. The wing-body combination was composed of a cruciform arrangement of two identical triangular wings of aspect ratio 2.31 corresponding to a leading-edge sweep angle of 60°, placed 'on a body of fineness ratio of 16. The investigation was conducted at a Mach number of 1.40 and at a Reynolds number of 1.25 million based on the mean aerodynamic chord of the wings. Dawnwash and sidewash measurements were made for angles of bank of O°, 11-1/4°, 22-1/2°, and 45° and through an angle-of-attack range of ±8O°.
This report presents the results of wind tunnel tests of a wing in combination with each of three sizes of Fowler flap. The purpose of the investigation was to determine the aerodynamic characteristics as affected by flap chord and position, the air loads on the flaps, and the effect of flaps on the downwash.
The theory of wind tunnel boundary influence on the downwash from a wing has been extended to provide more complete corrections for application to airplane test data. The first section of the report gives the corrections of the lifting line for wing positions above or below the tunnel center line; the second section shows the manner in which the induced boundary influence changes with distance aft of the lifting line. Values of the boundary corrections are given for off-center positions of the wing in circular, square, 2:1 rectangular, and 2:1 elliptical tunnels. Aft of the wing the corrections are presented for only the square and the 2:1 rectangular tunnels, but it is believed that these may be applied to jets of circular and 2:1 elliptical cross sections. In all cases results are included for both open and closed tunnels.
A theoretical study was made of the reduction in downwash and the upward displacement of the wake in the presence of the ground, and some verification of theory was obtained by means of air-flow measurements made with a ground-board and image-wing combination. Methods are given for estimating the effects and numerous examples are included to illustrate the nature of these effects and to show their order of magnitude.
This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.
This report treats the Kernel function of the integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for harmonically oscillating wings in supersonic flow. The treatment is essentially an extension to supersonic flow of the treatment given in NACA report 1234 for subsonic flow. For the supersonic case the Kernel function is derived by use of a suitable form of acoustic doublet potential which employs a cutoff or Heaviside unit function. The Kernel functions are reduced to forms that can be accurately evaluated by considering the functions in two parts: a part in which the singularities are isolated and analytically expressed, and a nonsingular part which can be tabulated.
An investigation of the nature of the flow field behind a rectangular wing of circular arc cross section has been conducted in the Langley 9-inch supersonic tunnel. Pitot- and static-pressure surveys covering a region of flow behind the wing have been made together with detailed pitot surveys throughout the region of the wake. In addition, the flow direction has been measured by means of a weathercocking vane. Theoretical calculations have been made to obtain the variation of both downwash and sidewash with angle of attack by using the superposition method of Lagerstrom, Graham, and Grosslight. In addition, the effect of wing thickness on the sidewash with the wing at 0 degree angle of attack has been evaluated.
The new downwash measurements behind a tapered wing with parallel center section described in the present report can be brought into good agreement with theoretical calculations if made on the basis of not-rolled-up vortex sheet and allowance is made for the lowering of the sheet. The test values are about 1 degree higher than the "upper limit" established for it, as against approximately 0.5 degrees in the earlier tests behind a rectangular and elliptical wing. The measurements on lateral axes, especially if lying below the wing on a level with the vortex train, disclosed in accord with the lift distribution, a marked change in angle over the span of the tail in contrast to the rectangular and elliptical wing.
A solution has been obtained for the complete tunnel-interference flow for a lifting vortex in a two-dimensional slotted tunnel. Curves are presented for the longitudinal distribution of tunnel-induced downwash angle for various values of the boundary openness parameter and for various heights of the vortex above the tunnel center line. Some quantitative discussion is given of the use of these results in calculating the tunnel interference for three-dimensional wings in rectangular tunnels with closed side walls and slotted top and bottom.