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  Partner: UNT Libraries Government Documents Department
 Decade: 1940-1949
 Serial/Series Title: NACA Technical Reports
 Collection: National Advisory Committee for Aeronautics Collection
The Lagrangian Multiplier Method of Finding Upper and Lower Limits to Critical Stresses of Clamped Plates

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

Date: January 1, 1946
Creator: Hu, Pai C. & Budiansky, Bernard
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.
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Lifting-surface-theory aspect-ratio corrections to the lift and hinge-moment parameters for full-span elevators on horizontal tail surfaces

Lifting-surface-theory aspect-ratio corrections to the lift and hinge-moment parameters for full-span elevators on horizontal tail surfaces

Date: January 1, 1948
Creator: Crandall, Stewart M & Swanson, Robert S
Description: A limited number of lifting-surface-theory solutions for wings with chordwise loadings resulting from angle of attack, parabolic-ac camber, and flap deflection are now available. These solutions were studied with the purpose of determining methods of extrapolating the results in such a way that they could be used to determine lifting-surface-theory values of the aspect-ratio corrections to the lift and hinge-moment parameters for both angle-of-attack and flap-deflection-type loading that could be used to predict the characteristics of horizontal tail surfaces from section data with sufficient accuracy for engineering purposes. Such a method was devised for horizontal tail surfaces with full-span elevators. In spite of the fact that the theory involved is rather complex, the method is simple to apply and may be applied without any knowledge of lifting-surface theory. A comparison of experimental finite-span and section value and of the estimated values of the lift and hinge-moment parameters for three horizontal tail surfaces was made to provide an experimental verification of the method suggested. (author).
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An investigation of the drag of windshields in the 8-foot high-speed wind tunnel

An investigation of the drag of windshields in the 8-foot high-speed wind tunnel

Date: January 1, 1942
Creator: Robinson, Russell G & Delano, James B
Description: Report presents the results of tests made to determine the drag of closed-cockpit and transport-type windshields. The tests were made at speeds corresponding to a Mach number range of approximately 0.25 to 0.58 in the NACA 8-foot high-speed wind tunnel. This speed range corresponds to a test Reynolds number range of 2,510,000 to 4,830,000 based on the mean aerodynamic chord of the full-span model (17.29 in.). The shapes of the windshield proper, the hood, and the tail fairing were systematically varied to include common types and refined design.
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On the use of residue theory for treating the subsonic flow of a compressible fluid

On the use of residue theory for treating the subsonic flow of a compressible fluid

Date: January 1, 1942
Creator: Kaplan, Carl
Description: A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.
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A study by high-speed photography of combustion and knock in a spark-ignition engine

A study by high-speed photography of combustion and knock in a spark-ignition engine

Date: January 1, 1942
Creator: Miller, Cearcy D
Description: The study of combustion in a spark-ignition engine given in Technical Report no. 704 has been continued. The investigation was made with the NACA high-speed motion-picture camera and the NACA optical engine indicator. The camera operates at the rate of 40,000 photographs a second and makes possible the study of phenomena occurring in time intervals as short as 0.000025 second. Photographs are presented of combustion without knock and with both light and heavy knocks, the end zone of combustion being within the field of view. Time-pressure records covering the same conditions as the photographs are presented and their relations to the photographs are studied. Photographs with ignition at various advance angles are compared with a view to observing any possible relationship between pressure and flame depth. A tentative explanation of knock is suggested, which is designed to agree with the indications of the high-speed photographs and the time-pressure records.
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Determination of optimum plan forms for control surfaces

Determination of optimum plan forms for control surfaces

Date: January 1, 1942
Creator: Jones, Robert T & Cohen, Doris
Description: Solutions found for a range of airfoil plan forms indicate that, regardless of the characteristics of the tail surface, the chord of the rudder or of the elevator should be very nearly constant over its span. The optimum ailerons are also of a characteristic shape, varying little with the plan form of the wing.
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Pressure distribution over an NACA 23012 airfoil with a fixed slot and a slotted flap

Pressure distribution over an NACA 23012 airfoil with a fixed slot and a slotted flap

Date: January 1, 1942
Creator: Harris, Thomas A & Lowry, John G
Description: Report presents the results of a pressure-distribution investigation conducted in the Langley Memorial Aeronautical Laboratory 7 by 10-foot wind tunnel to determine the air loads on an NACA 23012 airfoil in combination with a fixed leading-edge slot and a slotted flap. Pressures were measured over the upper and lower surfaces of the component parts of the combination for several angles of attack and at several flap settings. The data, presented as pressure diagrams and graphs of section coefficients, are applicable to rib, slat, and flap designs for the combination.
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Critical Compressive Stress for Outstanding Flanges

Critical Compressive Stress for Outstanding Flanges

Date: January 1, 1942
Creator: Lundquist, Eugene E & Stowell, Elbridge Z
Description: A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in outstanding flanges. These flanges are flat rectangular plates supported along the loaded edges, supported and elastically restrained along one unloaded edge, and free along the other unloaded edge. The mathematical derivations of the formulas required for construction of the chart are given.
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Test of single-stage axial-flow fan

Test of single-stage axial-flow fan

Date: January 1, 1942
Creator: Bell, E Barton
Description: A single-stage axial fan was built and tested in the shop of the propeller-research tunnel of the NACA. The fan comprised a simple 24-blade rotor having a diameter of 21 inches and a solidity of 0.86 and a set of 37 contravanes having a solidity of 1.33. The rotor was driven by a 25-horsepower motor capable of rotating at a speed of 3600 r.p.m. The fan was tested for volume, pressure, and efficiency over a range of delivery pressures and volumes for a wide range of contravane and blade-angle settings. The test results are presented in chart form in terms of nondimensional units in order that similar fans may be accurately designed with a minimum effort. The maximum efficiency (88 percent) was obtained by the fan at a blade angle of 30 degrees and a contravane angle of 70 degrees. An efficiency of 80 percent was obtained by the fan with the contravanes removed.
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Effect of body nose shape on the propulsive efficiency of a propeller

Effect of body nose shape on the propulsive efficiency of a propeller

Date: January 1, 1941
Creator: Stickle, George W; Crigler, John L & Naiman, Irven
Description: Report presents the results of an investigation of the propulsive efficiency of three adjustable propellers of 10-foot diameter operated in front of four body nose shapes, varying from streamline nose that continued through the propeller plane in the form of a large spinner to a conventional open-nose radial-engine cowling. One propeller had airfoil sections close to the hub, the second had conventional round blade shanks, and the third differed from the second only in pitch distribution. The blade-angle settings ranged from 20 degrees to 55 degrees at the 0.75 radius. The effect of the body nose shape on propulsive efficiency may be divided into two parts: (1) the change in the body drag due to the propeller slipstream and (2) the change in propeller load distribution due to the change in velocity caused by the body. For the nose shape tested in the report, the first effect is shown to be very small; therefore, the chief emphasis of the report is confined to the second effect.
Contributing Partner: UNT Libraries Government Documents Department
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