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The Lagrangian Multiplier Method of Finding Upper and Lower Limits to Critical Stresses of Clamped Plates

Description: The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the truss, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Raleigh-Rite method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems problems the Lagrangian multiplier method finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.
Date: January 1, 1946
Creator: Hu, Pai C. & Budiansky, Bernard
Partner: UNT Libraries Government Documents Department

Flow over a slender body of revolution at supersonic velocities

Description: The theory of small disturbances is applied to the calculation of the pressure distribution and drag of a closed body of revolution traveling at supersonic speeds. It is shown that toward the rear of the body the shape of the pressure distribution is similar to that for subsonic flow. For fineness ratios between 10 and 15 the theoretical wave drag is of the same order as probable values of the frictional drag.
Date: July 8, 1946
Creator: Jones, Robert T & Margolis, Kenneth
Partner: UNT Libraries Government Documents Department

Wind-tunnel investigation of end-plate effects of horizontal tails on a vertical tail compared with available theory

Description: A vertical-tail model with stub fuselage was tested in combination with various simulated horizontal tails to determine the effect of horizontal-tail span and location on the aerodynamic characteristics of the vertical tail. Available theoretical data on end-plate effects were collected and presented in the form most suitable for design purposes. Reasonable agreement was obtained between the measured and theoretical end-plate effects of horizontal tails on vertical tails, and the data indicated that the end-plate effect was determined more by the location of the horizontal tail than by the span of the horizontal tail. The horizontal tail gave most end-plate effect when located near either tip of the vertical tail and, when located near the base of the vertical tail, the end-plate effect was increased by moving the horizontal tail rearward.
Date: January 21, 1946
Creator: Murray, Harry E.
Partner: UNT Libraries Government Documents Department

Bending-torsion flutter calculations modified by subsonic compressibility corrections

Description: A number of calculations of bending-torsion wing flutter are made at two Mach numbers, m=0 (incompressible case) and m=0.7, and results are compared. The air forces employed for the case of m=0.7 are based on Frazer's recalculation of Possio's results, which are derived on the assumption of small disturbances to the main flow. For ordinary wings of normal density and of low bending frequency in comparison with torsion frequency, the compressibility correction to the flutter speed appears to be of the order of a few percent; whereas the correction to flutter speed for high-density wing sections, such as propeller sections, and to the wing-divergence speed in general, may be based on a rule using the (1 - m(2))1/4 factor and, for m=0.7, represents a decrease of the order of 17 percent.
Date: January 1, 1946
Creator: Garrick, I E
Partner: UNT Libraries Government Documents Department

Flutter and oscillating air-force calculations for an airfoil in two-dimensional supersonic flow

Description: A connected account is given of the Possio theory of non-stationary flow for small disturbances in a two-dimensional supersonic flow and of its application to the determination of the aerodynamic forces on an oscillating airfoil. Further application is made to the problem of wing flutter in the degrees of freedom - torsion, bending, and aileron rotations. Numerical tables for flutter calculations are provided for various values of the Mach number greater than unity. Results for bending-torsion wing flutter are shown in figures and are discussed. The static instabilities of divergence and aileron reversal are examined as is a one-degree-of-freedom case of torsional oscillatory instability.
Date: October 1, 1946
Creator: Garrick, I E & Rubinow, S I
Partner: UNT Libraries Government Documents Department

Properties of low-aspect-ratio pointed wings at speeds below and above the speed of sound

Description: Low-aspect-ratio wings having pointed plan forms are treated on the assumption that the flow potentials in planes at right angles to the long axis of the airfoils are similar to the corresponding two-dimensional potentials. For the limiting case of small angles of attack and low aspect ratios the theory brings out the following significant properties: (1) The lift of a slender, pointed airfoil moving in the direction of its long axis depends on the increase in width of the sections in a downstream direction. Sections behind the section of maximum width develop no lift. (2) The spanwise loading of such an airfoil is independent of the plan form and approaches the distribution giving a minimum induced drag. (3) The lift distribution of a pointed airfoil travelling point-foremost is relatively unaffected by the compressibility of the air below or above the speed of sound. A best of a triangular airfoil at a Mach number of 1.75 verified the theoretical values of lift and center of pressure.
Date: January 1, 1946
Creator: Jones, Robert T.
Partner: UNT Libraries Government Documents Department

On laminar and turbulent friction

Description: Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author).
Date: September 1, 1946
Creator: Von Karman, TH
Partner: UNT Libraries Government Documents Department

The development of a lateral-control system for use with large-span flaps

Description: A spoiler-type lateral-control system has been developed for use on the Northrop P-61 airplane. The lateral-control system is to be used with large-span flaps and consists of a thin circular arc spoiler, linked with a short-span plain aileron located just outboard of the spoiler. This unconventional lateral-control system has been accepted with enthusiasm by the pilots who have flown the airplane. The particularly appreciate its characteristic at high speed. The combination of light forges, favorable yawing moment, and low wing torsional moments, make it a very effective, easily applied control. The control available at and through the stall is also remarkably good, although this characteristic may be attributed, in part, to an exceptionally good wing stalling pattern rather than entirely to the use of the spoiler-type aileron. In the landing configuration, the lateral-control effectiveness increases automatically with the extension of wing flaps so that powerful control is available during the approach. There is, however, a decrease in effectiveness for the first 5 percent of the wheel travel with a resultant tendency for inexperienced pilots to overcontrol slightly at low speeds. The fact that the aileron can be fully used at the stall, however, more than compensates for this loss of effectiveness with flaps down and greatly enhances the airplane's landing performance.
Date: January 1, 1946
Creator: Ashkenas, I L
Partner: UNT Libraries Government Documents Department

Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

Description: This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The ...
Date: January 1, 1946
Creator: Hoff, N J; Libby, Paul A & Klein, Bertran
Partner: UNT Libraries Government Documents Department

Stresses in and general instability of monocoque cylinders with cutouts I : experimental investigation of cylinders with a symmetric cutout subjected to pure bending

Description: Ten 24S-T alclad cylinders of 20-inch diameter, 45- or 58-inch length, and 0.012-inch wall thickness, reinforced with 24S-T aluminum alloy stringers and rings were tested in pure bending. In the middle of the compression side of the cylinders there was a cutout extending over 19 inches in the longitudinal direction, and over an angle of 45 degrees, 90 degrees, or 135 degrees in the circumferential direction. The strain in the stringers and in the sheet covering was measured with metal electric strain gages. The stress distribution in the cylinders deviate considerably from the linear law valid for cylinders without a cutout. The maximum strain measured was about four-thirds of the value calculated from the Mc/I formula when I was taken as the moment of inertia of the cross section of the portion of the cylinder where the cutout was situated. A diagram is presented containing the strain factors defined as the ratios of measured strain to strain calculated with the Mc/I formula. All the 10 cylinders tested failed in general instability. Two symmetric and one antisymmetric pattern of buckling were observed and the buckling load appeared to be independent of the method of manufacture and the length of the cylinder. The buckling load of the cylinders having cutouts extending over 45 degrees, 90 degrees, and 135 degrees was 66, 47, and 31 percent, respectively, of the buckling load of the cylinder without a cutout.
Date: January 1, 1946
Creator: Hoff, N J & Boley, Bruno A
Partner: UNT Libraries Government Documents Department

Tank tests to determine the effect on planing-tail hulls of varying length, width, and plan-form taper of afterbody

Description: Tests were conducted in Langley Tank no. 2 on models of an unconventional flying-boat hull called a planing-tail hull to determine the effects on resistance of varying a number of afterbody parameters. The effects of varying length, width, and plan-form taper of the afterbody are presented. Tests were made with afterbodies of two widths, two lengths, and two tapers. In the tests the depth of step and the angle of afterbody keel were held constant.(author).
Date: January 1, 1946
Creator: Dawson, John R; Walter, Robert C & Hay, Elizabeth S
Partner: UNT Libraries Government Documents Department