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**Partner:**UNT Libraries Government Documents Department

**Decade:**1940-1949

**Serial/Series Title:**NACA Technical Reports

### 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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### A Theoretical Investigation of Longitudinal Stability of Airplanes with Free Controls Including Effect of Friction in Control System

**Date:**January 1, 1944

**Creator:**Greenberg, Harry & Sternfield, Leonard

**Description:**The relation between the elevator hinge moment parameters and the control forces for changes in forward speed and in maneuvers is shown for several values of static stability and elevator mass balance. The stability of the short period oscillations is shown as a series of boundaries giving the limits of the stable regions in terms of the elevator hinge moment parameters. The effects of static stability, elevator moment of inertia, elevator mass unbalance, and airplane density are also considered. Dynamic instability is likely to occur if there is mass unbalance of the elevator control system combined with a small restoring tendency (high aerodynamic balance). This instability can be prevented by a rearrangement of the unbalancing weights which, however, involves an increase of the amount of weight necessary. It can also be prevented by the addition of viscous friction to the elevator control system provided the airplane center of gravity is not behind a certain critical position. For high values of the density parameter, which correspond to high altitudes of flight, the addition of moderate amounts of viscous friction may be destabilizing even when the airplane is statically stable. In this case, increasing the viscous friction makes the oscillation stable again. ...

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### 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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### A method of estimating the knock rating of hydrocarbon fuel blend

**Date:**January 1, 1943

**Creator:**Sanders, Newell D

**Description:**The usefulness of the knock ratings of pure hydrocarbon compounds would be increased if some reliable method of calculating the knock ratings of fuel blends was known. The purpose of this study was to investigate the possibility of developing a method of predicting the knock ratings of fuel blends.

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### The Measurement of Fuel-Air Ratio by Analysis for the Oxidized Exhaust Gas

**Date:**January 1, 1943

**Creator:**Gerrish, Harold C. & Meem, J. Lawrence, Jr.

**Description:**An investigation was made to determine a method of measuring fuel-air ratio that could be used for test purposes in flight and for checking conventional equipment in the laboratory. Two single-cylinder test engines equipped with typical commercial engine cylinders were used. The fuel-air ratio of the mixture delivered to the engines was determined by direct measurement of the quantity of air and of fuel supplied and also by analysis of the oxidized exhaust gas and of the normal exhaust gas. Five fuels were used: gasoline that complied with Army-Navy fuel Specification No. AN-VV-F-781 and four mixtures of this gasoline with toluene, benzene, and xylene. The method of determining the fuel-air ratio described in this report involves the measurement of the carbon-dioxide content of the oxidized exhaust gas and the use of graphs for the presented equation. This method is considered useful in aircraft, in the field, or in the laboratory for a range of fuel-air ratios from 0.047 to 0.124.

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### Tests of the NACA 0025 and 0035 airfoils in the full-scale wind tunnel

**Date:**January 1, 1941

**Creator:**Bullivant, W Kenneth

**Description:**This report presents the results of an investigation conducted in the NACA full-scale wind tunnel to determine the aerodynamic characteristics of the 6 by 36-foot rectangular NACA 0025 and 0035 airfoils. The aerodynamic characteristics of the plain airfoils with rounded and square tips were determined by force tests through a complete angle-of-attack range, in addition, the profile drag was determined by the momentum method. The transition points on the airfoils were located by boundary-layer determinations with small total-head and static tubes. Each airfoil was also tested with a 0.20c full-span split flap. Tuft surveys were included to show the progressive breakdown of flow with increasing angles of attack. Previously published data from tests of the NACA 0009, 0012, and 0018 airfoils in the full-scale tunnel have been included in the summary curves.

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### Wind-tunnel investigation of spoiler, deflector, and slot lateral-control devices on wings with full-span split and slotted flaps

**Date:**January 1, 1941

**Creator:**Wenzinger, Carl J & Rogallo, Francis M

**Description:**Report presents the results of an extensive investigation made in the NACA 7 by 10-foot wind tunnel of spoiler, deflector, and slot types of lateral-control device on wings with full-span split and slotted flaps. The static rolling and yawing moments were determined for all the devices tested, and the static hinge moments and the time response were determined for a few devices of each type.

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### Preliminary wind-tunnel investigation of an NACA 23012 airfoil with various arrangements of venetian-blind flaps

**Date:**January 1, 1940

**Creator:**Wenzinger, Carl J & Harris, Thomas A

**Description:**Report presents the results of an investigation made in the NACA 7 by 10-foot wind tunnel of a large-chord NACA 23012 airfoil with several arrangements of venetian-blind flaps to determine the aerodynamic section characteristics as affected by the over-all flap chord, the chords of the slats used to form the flap, the slat spacing, the number of slats and the position of the flap with respect to the wing. Complete section data are given in the form of graphs for all the combinations tested.

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### Mechanism of flutter.a theoretical and experimental investigation of the flutter problem

**Date:**January 1, 1940

**Creator:**Theodorsen, Theodore & Garrick, I E

**Description:**The results of the basic flutter theory originally devised in 1934 and published as NACA Technical Report no. 496 are presented in a simpler and more complete form convenient for further studies. The paper attempts to facilitate the judgement of flutter problems by a systematic survey of the theoretical effects of the various parameters. A large number of experiments were conducted on cantilever wings, with and without ailerons, in the NACA high-speed wind tunnel for the purpose of verifying the theory and to study its adaptability to three-dimensional problems. The experiments included studies on wing taper ratios, nacelles, attached floats, and external bracings. The essential effects in the transition to the three-dimensional problem have been established. Of particular interest is the existence of specific flutter modes as distinguished from ordinary vibration modes. It is shown that there exists a remarkable agreement between theoretical and experimental results.

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### General Theory of Aerodynamic Instability and the Mechanism of Flutter

**Date:**January 1, 1949

**Creator:**Theodorsen, Theodore

**Description:**The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom have been determined. The problem resolves itself into the solution of certain definite integrals, which have been identified as Bessel functions of the first and second kind and of zero and first order. The theory, being based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing-section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been arrived at. The solution is of a simple form and is expressed by means of an auxiliary parameter K.

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### Theoretical lift and drag of thin triangular wings at supersonic speeds

**Date:**January 1, 1946

**Creator:**Brown, Clinton E

**Description:**A method is derived for calculating the lift and the drag due to lift of point-forward triangular wings and a restricted series of sweptback wings at supersonic speeds. The elementary or "supersonic sources" solution of the linearized equation of motion is used to find the potential function of a line of doublets. The flow about the triangular flat plate is then obtained by a surface distribution of these doublet lines. The lift-curve slope of triangular wings is found to be a function of the ratio of the tangent of the apex angle to the tangent of the Mach angle. As the apex angle approaches and becomes greater than the Mach angle, the lift coefficient of the triangular wing becomes equal to that of a two-dimensional supersonic airfoil at the same Mach number. The drag coefficient due to lift of triangular wings with leading edges well behind the Mach cone is shown to be close to that of elliptically loaded wings of the same aspect ratio in subsonic flight. The resultant force on wings with leading edges outside the Mach cone, however, is shown to act normal to the surfaces and thus an induced drag equal to the lift times the ...

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### Free-spinning wind-tunnel tests of a low-wing monoplane with systematic changes in wings and tails V : effect of airplane relative density

**Date:**January 1, 1940

**Creator:**Seidman, Oscar & Neihouse, A I

**Description:**The reported tests are a continuation of an NACA investigation being made in the free-spinning wind tunnel to determine the effects of independent variations in load distribution, wing and tail arrangement, and control disposition on the spin characteristics of airplanes. The standard series of tests was repeated to determine the effect of airplane relative density. Tests were made at values of the relative-density parameter of 6.8, 8.4 (basic), and 12.0; and the results were analyzed. The tested variations in the relative-density parameter may be considered either as variations in the wing loading of an airplane spun at a given altitude, with the radii of gyration kept constant, or as a variation of the altitude at which the spin takes place for a given airplane. The lower values of the relative-density parameter correspond to the lower wing loadings or to the lower altitudes of the spin.

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### Internal-flow systems for aircraft

**Date:**January 1, 1941

**Creator:**Rogallo, F M

**Description:**An investigation has been made to determine efficient arrangements for an internal-flow system of an aircraft when such a system operates by itself or in combination with other flow systems. The investigation included a theoretical treatment of the problem and tests in the NACA 5-foot vertical wind tunnel of inlet and outlet openings in a flat plate and in a wing.

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### Investigations on the incompletely developed plane diagonal-tension field

**Date:**January 1, 1940

**Creator:**Kuhn, Paul

**Description:**This report presents the results of an investigation on the incompletely developed diagonal-tension field. Actual diagonal-tension beams work in an intermediate stage between pure shear and pure diagonal tension; the theory developed by wagner for diagonal tension is not directly applicable. The first part of the paper reviews the most essential items of the theory of pure diagonal tension as well as previous attempts to formulate a theory of incomplete diagonal tension. The second part of the paper describes strain measurement made by the N. A. C. A. to obtain the necessary coefficients for the proposed theory. The third part of the paper discusses the stress analysis of diagonal-tension beams by means of the proposed theory.

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### The unsteady lift of a wing of finite aspect ratio

**Date:**January 1, 1940

**Creator:**Jones, Robert T

**Description:**Unsteady-lift functions for wings of finite aspect ratio have been calculated by correcting the aerodynamic inertia and the angle of attack of the infinite wing. The calculations are based on the operational method.

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### A unified theory of plastic buckling of columns and plates

**Date:**January 1, 1948

**Creator:**Stowell, Elbridge Z

**Description:**On the basis of modern plasticity considerations, a unified theory of plastic buckling applicable to both columns and plates has been developed. For uniform compression, the theory shows that long columns which bend without appreciable twisting require the tangent modulus and that long flanges which twist without appreciable bending require the secant modulus. Structures that both bend and twist when they buckle require a modulus which is a combination of the secant modulus and the tangent modulus.

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### Stability of Castering Wheels for Aircraft Landing Gears

**Date:**January 1, 1940

**Creator:**Kantrowitz, Arthur

**Description:**A theoretical study was made of the shimmy of castering wheels. The theory is based on the discovery of a phenomenon called kinematic shimmy. Experimental checks, use being made of a model having low-pressure tires, are reported and the applicability of the results to full scale is discussed. Theoretical methods of estimating the spindle viscous damping and the spindle solid friction necessary to avoid shimmy are given. A new method of avoiding shimmy -- lateral freedom -- is introduced.

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### Thin oblique airfoils at supersonic speed

**Date:**January 1, 1946

**Creator:**Jone, Robert T

**Description:**The well-known methods of thin-airfoil theory have been extended to oblique or sweptback airfoils of finite aspect ratio moving at supersonic speeds. The cases considered thus far are symmetrical airfoils at zero lift having plan forms bounded by straight lines. Because of the conical form of the elementary flow fields, the results are comparable in simplicity to the results of the two-dimensional thin-airfoil theory for subsonic speeds. In the case of untapered airfoils swept back behind the Mach cone the pressure distribution at the center section is similar to that given by the Ackeret theory for a straight airfoil. With increasing distance from the center section the distribution approaches the form given by the subsonic-flow theory. The pressure drag is concentrated chiefly at the center section and for long wings a slight negative drag may appear on outboard sections. (author).

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### Summary of lateral-control research

**Date:**January 1, 1947

**Creator:**Toll, Thomas A

**Description:**A summary has been made of the available information on lateral control. A discussion is given of the criterions used in lateral-control specifications, of the factors involved in obtaining satisfactory lateral control, and of the methods employed in making lateral-control investigations in flight and in wind tunnels. The available data on conventional flap-type ailerons having various types of aerodynamic balance are presented in a form convenient for use in design. The characteristics of spoiler devices and booster mechanisms are discussed. The effects of Mach number, boundary layer, and distortion of the wing or of the lateral-control system are considered insofar as the available information permits. An example is included to illustrate the use of the design data. The limitations of the available information and some of the lateral-control problems that remain to be solved are indicated.

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### Application of the method of characteristics to supersonic rotational flow

**Date:**January 1, 1946

**Creator:**Ferri, Antonio

**Description:**A system for calculating the physical properties of supersonic rotational flow with axial symmetry and supersonic rotational flow in a two-dimensional field was determined by use of the characteristics method. The system was applied to the study of external and internal flow for supersonic inlets with axial symmetry. For a circular conical inlet the shock that occurred at the lip of the inlet became stronger as it approached the axis of the inlet and became a normal shock at the axis. The region in which strong shock occurred increased with increase of the angle of internal cone at the lip of the inlet. For an inlet with a central body the method of characteristics was applied to the design of an internal channel shape that, theoretically, results in very efficient recompression in the inlet. It was shown that if an effuser is connected with the diffuser a body of revolution with very small shock-wave drag can be determined. (author).

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### Pressure distribution over NACA 23012 airfoil with a slotted and a split flap

**Date:**January 1, 1941

**Creator:**Harris, Thomas A & Lowry, John G

**Description:**A pressure-distribution investigation has been conducted in the NACA 4 by 6-foot vertical wind tunnel to determine the air loads on an NACA 23012 airfoil in combination with a 25.66-percent-chord slotted flap and a 20-percent-chord split flap. Pressures were measured on both the upper and the lower surfaces of the main airfoil and the flaps for several angles of attack and at several flap settings. The data, presented as pressure diagrams and as graphs of the section coefficients for the flap alone and for the airfoil-flap combinations, are applicable to rib and flap design for a combination of a thick airfoil and a slotted or a split flap. The results of previous tests of a NACA 23012 airfoil with a slotted flap are compared with the present results.

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### A simplified theoretical method of determining the characteristics of a lifting rotor in forward flight

**Date:**January 1, 1941

**Creator:**Bailey, F J , Jr

**Description:**Theoretical derived expressions for the flapping, the thrust, the torque, and the profile drag-lift ratio of nonfeathering rotor with hinged, rectangular, linearly twisted blades are given as simple functions of the inflow velocity and the blade pitch. Representative values of the coefficients of each of the terms in these expressions are tabulated for a series of specified values of the tip-speed ratio. Analysis indicates that the tabulated values can be used to calculate, with reasonable accuracy, the characteristics of any rotor of conventional design.

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### Correlation of cooling data from an air-cooled cylinder and several multicylinder engines

**Date:**January 1, 1940

**Creator:**Pinkel, Benjamin & Ellerbrock, Herman H , Jr

**Description:**The theory of engine-cylinder cooling developed in a previous report was further substantiated by data obtained on a cylinder from a Wright r-1820-g engine. Equations are presented for the average head and barrel temperatures of this cylinder as functions of the engine and the cooling conditions. These equations are utilized to calculate the variation in cylinder temperature with altitude for level flight and climb. A method is presented for correlating average head and barrel temperatures and temperatures at individual points on the head and the barrel obtained on the test stand and in flight. The method is applied to the correlation and the comparison of data obtained on a number of service engines. Data are presented showing the variation of cylinder temperature with time when the power and the cooling pressure drop are suddenly changed.

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### Preignition characteristics of several fuels under simulated engine conditions

**Date:**January 1, 1941

**Creator:**Spencer, R C

**Description:**The preignition characteristics of a number of fuels have been studied under conditions similar to those encountered in an engine. These conditions were simulated by suddenly compressing a fuel-air mixture in contact with an electrically heated hot spot in the cylinder head of the NACA combustion apparatus. Schlieren photographs and indicator cards were taken of the burning, and the hot-spot temperatures necessary to cause ignition under various conditions were determined.

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