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Theory of automatic control of airplanes
Methods of automatically controlling the airplane are reviewed. Equations for the controlled motion including inertia effects of the control are developed and methods of investigating the stability of the resulting fifth and higher order equations are presented. The equations for longitudinal and lateral motion with both ideal and non-ideal controls are developed in dimensionless form in terms of control parameters based on simple dynamic tests of the isolated control unit.
Theory of Characteristics
The theory of characteristics will be presented generally for quasilinear differential equations of the second order in two variables. This is necessary because of the manifold requirements to be demanded from the theory of characteristics.
A theory of conductivity of cold-worked copper
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The theory of contra-vanes applied to the propeller
The optimum circulation distribution and hence the maximum theoretical thrust obtainable for contra-vanes fitted behind propellers is markedly dependent on the number of guide vanes. The outer portion of the vanes, even if projecting considerably beyond the edge of the propeller slipstream, still contribute appreciably to this theoretical gain of thrust. But, owing to the always existing friction of the vanes, the limit of the optimum vane length lies at relatively small diameters. A large hub unloads the vanes. Hence, the guide vanes are best attached to suitable parts of the bodies which would, in any case, be subjected to the slipstream.
Theory of Determination of Ultra-Radio Frequencies by Standing Waves on Wires
Scientific paper issued by the Bureau of Standards over ultra-radio frequencies. As stated in the abstract, "this paper furnishes the theoretical background for the method of frequency standardization employing short standing waves on parallel wires" (p. 487). This paper includes tables, and illustrations.
The theory of diffusion in strained systems
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Theory of dynamic creep
An analysis is given of the causes of the increase in the creep of a material under dynamic loads. A theory of dynamic creep is proposed based on the after-effect theory of Becker.
Theory of flame propagation
The mechanism of flame propagation has been qualitatively formulated. In accordance with this formulation, the chemical reaction initiated in some layer brings about an increase in the temperature; because of the heat conduction, the temperature is raised in the neighboring layer where in turn the chemical reaction is initiated. In this manner the flame is propagated.
Theory of flapping flight
Before attempting to construct a human-powered aircraft, the aviator will first try to post himself theoretically on the possible method of operating the flapping wings. This report will present a graphic and mathematical method, which renders it possible to determine the power required, so far as it can be done on the basis of the wing dimensions. We will first consider the form of the flight path through the air. The simplest form is probably the curve of ordinary wave motion. After finding the flight curve, we must next determine the change in the angle of attack while passing through the different phases of the wave.
Theory of ground vibrations of a two-blade helicopter rotor on anisotropic flexible supports
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Theory of heat transfer and hydraulic resistance of oil radiators
In the present report the coefficients of heat transfer and hydraulic resistance are theoretically obtained for the case of laminar flow of a heated viscous liquid in a narrow rectangular channel. The results obtained are applied to the computation of oil radiators, which to a first approximation may be considered as made up of a system of such channels. In conclusion, a comparison is given of the theoretical with the experimental results obtained from tests on airplane oil radiators.
Theory of Heat Transfer in Smooth and Rough Pipes
The heat transfer accompanying turbulent flow in tubes has been treated by a new theory of wall turbulence, and a formula for smooth tubes has been derived which is asymptotic at Re approaches infinity. It agrees very well with the data available to date. The formula also holds for the flow along a flat plate if lambda is based on the velocity far away. For rough tubes, the unit conductance is shown to be a function of kv*/upsilon; the two empirical constants (delta(r), n) which appear in equation (52) cannot yet be determined because of lack of experimental data.
Theory of helicopter damping in pitch or roll and a comparison with flight measurements
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Theory of lifting surfaces
The general basis of the theory of lifting surfaces is discussed. The problem of the flow of a fluid about a lifting surface of infinite span is examined in terms of the existence of vortexes in the current. A general theory of permanent flow is discussed. Formulas for determining the influence of aspect ratio that may be applied to all wings, whatever their plane form, are given.
Theory of Lifting Surfaces, Part 2
A mathematical model is presented towards a theory of lifting and resistance on wings. It consists of a theory of multiplanes, conditions of flow at a great distance from the wing, lifting systems of minimum resistance, and free stream and stream limited by walls.
Theory of mechanical oscillations of rotors with two hinged blades
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Theory of plane, symmetrical intake diffusers
The present report ties in with the investigations on the inlet diffusers by P. Ruden. The theory developed by Ruden had produced results which found excellent confirmation in wind-tunnel tests and in spite of certain still-existing defects, are technically very promising. The reasons for the new theory of the diffuser forms indicated by Ruden are twofold: first, the arguments adduced in Ruden's theory deal only with one specific operating condition, that is, a certain ratio of mean velocity within the diffuser to flying speed, while in the present report any desired velocity ratios are involved; second, a different choice of parameters and the increased possibilities of variation result in diffuser forms which cannot be reconciled at once with Ruden's theory. The first enables a theoretical check of the measurements made with Ruden's diffusers at variable velocity ratio, the second permits the calculation of diffuser types which in many respects are superior to Ruden's diffusers.
The theory of plasticity in the case of simple loading accompanied by strain-hardening
The author has previously shown that a deformation theory of plasticity is entirely adequate when the loading is simple; that is, when all the applied forces grow in proportion to a single parameter. The author now shows how a general plasticitytheory for any complex loading may be constructed by successively adding quantities of the nature of correction terms to the deformation theory. All of the theories of plasticity so far suggested for the complex loading condition are shown to be special cases of this general theory.
The theory of propellers I : determination of the circulation function and the mass coefficient for dual-rotating propellers
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The theory of propellers I : determination of the circulation function and the mass coefficient for dual-rotating propellers
Values of the circulation function have been obtained for dual-rotating propellers. Numerical values are given for four, eight, and twelve-blade dual-rotating propellers and for advance ratios from 2 to about 6. In addition, the circulation function has been determine for single-rotating propellers for the higher values of the advance ratio. The mass coefficient, another quantity of significance in propeller theory, has been introduced.
The theory of propellers II : method for calculating the axial interference velocity
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The Theory of Propellers II : Method for Calculating the Axial Interference Velocity
A technical method is given for calculating the axial interference velocity of a propeller. The method involves the use of certain weight functions p, q, and f. Numerical values for the weight functions are given for two-blade, three-blade, and six-blade propellers.
The theory of propellers III : the slipstream contraction with numerical values for two-blade and four-blade propellers
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The Theory of Propellers III : the Slipstream Contraction with Numerical Values for Two-Blade and Four-Blade Propellers
As the conditions of the ultimate wake are concerned both theoretically and practically, the magnitude of the slipstream contraction has been calculated. It will be noted that the contraction in a representative case is of the order of only 1 percent of the propeller diameter. In consequence, all calculations need involve only first-order effects. Curves and tables are given for the contraction coefficient of two-blade and four-blade propellers for various values of the advance ratio; the contraction coefficient is defined as the contraction in the diameter of the wake helix in terms of the wake diameter at infinity. The contour lines of the wake helix are also shown at four values of the advance ratio in comparison with the contour lines for an infinite number of blades.
The theory of propellers IV : thrust, energy, and efficiency formulas for single- and dual-rotating propellers with ideal circulation distribution
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The theory of propellers IV : thrust, energy, and efficiency formulas for single and dual rotating propellers with ideal circulation distribution
Simple and exact expressions are given for the efficiency of single and dual rotating propellers with ideal circulation distribution as given by the Goldstein functions for single-rotating propellers and by the new functions for dual-rotating propellers from part I of the present series. The efficiency is shown to depend primarily on a defined load factor and, to a very small extent, on an axial loss factor. Tables and charts are included for practical use of the results.
Theory of reversible and nonreversible cracks in solids
The Griffith crack theory is reviewed and certain shortcomings of this theory are discussed. A new description for the shape of a crack is given which takes into account the atomic structure of material. Through consideration of the total energy of the system and the shape of the crack, expressions for crack behavior are derived which are considered to remedy the defects of the Griffith theory.
Theory of self-excited mechanical oscillations of helicopter rotors with hinged blades
Vibrations of rotary-wing aircraft may derive their energy from the rotation of the rotor rather than from the air forces. A theoretical analysis of these vibrations is described and methods for its application are explained in Chapter one. Chapter two reports the results of an investigation of the mechanical stability of a rotor having two vertically hinged blades mounted upon symmetrical supports, that is, of equal stiffness and mass in all horizontal directions. Chapter three presents the theory of ground vibrations of a two-blade helicopter rotor on anisotropic flexible supports.
Theory of Self-Excited Mechanical Oscillations of Helicopter Rotors with Hinged Blades
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Theory of self-excited mechanical oscillations of hinged rotor blades
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Theory of supersonic potential flow in turbomachines
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Theory of the ideal windmill
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Theory of the inlet and exhaust processes of internal-combustion engines
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Theory of the jet syphon
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Theory of the landing impact of seaplanes
The present investigation is an endeavor to express the jolting stresses, designated as landing impacts, undergone by seaplanes in landing and taking off from rough water, as functions of specific factors, in order to enable the evaluation of empirically obtained results and thus acquire theoretical data for the construction of seaplane floats and hulls.
The Theory of the Optical Wedge Beam Splitter
Report discussing optical wedge beam splitters and the basic theory for computing the ratio of the intensity of the incident beam to the intensity of any selected emerging beam and also for computing the direction of the emerging beam, assuming that the wedge angle, index of refraction, angle of incidence, and number of reflections are known.
The Theory of the Pitot and Venturi Tubes, Part 2
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The theory of the screw propeller
Given here is a brief review of the fundamental principles of the propeller slip-stream theory and its further development through later researches, which demonstrate the connection between the propeller slip-stream theory and Frounde's so-called 'propeller blade theory.' The propeller slip-stream theory, especially in its improved form, now gives us the basis for determining the mutual influence of the parts of the blade, so that, in calculating the shape of the blade, we can get along with certain section characteristics, which have been determined once and for all. It is argued that new theories present the possibility of investigating the phenomena in the vicinity of the propeller, allowing us to calculate its action on the basis of fewer experimental values.
Theory of the slotted wing
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The theory of the Strandgren cyclogyro
This report provides a description of the Standgren flying machine which consists of two wheels with a certain number of equidistant blades arranged around the horizontal axis of rotation and parallel to this axis. Each blade is fixed so as to be able to feather about an axis parallel to its span at the same time as it turns about the general axis of rotation. A general theory of wheels with blades rotating about a transverse axis is presented.
Theory of thin-walled rods
Starting with the Love equations for bending of extensible shells, "principal stress states" are sought for a thin-walled rod of arbitrary but open cross section. Principal stress states exclude those local states arising from end conditions which damp out with distance from the ends. It is found that for rods of intermediate length, long enough to avoid local bending at a support, and short enough that elementary torsion and bending are not the most significant stress states, four principal states exist. Three of these states are associated with the planar distribution of axial stress and are equivalent to the engineering theory of extension and bending of solid sections. The fourth state resembles that which has been called in the literature "bending stress due to torsional", except that cross sections are permitted to bend and the shear along the center line of the cross section is permitted to differ from zero.
Theory of two-dimensional potential flow about arbitrary wing sections
Three general theories treating the potential flow about an arbitrary wing section are discussed in this report. The first theory treats the method of conformal transformation as laid down by Theodorsen and Garrick; the second is a generalization of Birnbaum's theory for moderately thick airfoils; the third is a general investigation of the complex velocity function with particular reference to the relations first discussed by F. Weinig.
A Theory of Unstaggered Airfoil Cascades in Compressible Flow
By use of the methods of thin airfoil theory, which include effects of compressibility, rela.tio^as are developed which permit the rapid determination of the pressure distribution over an unstaggered cascade of airfoils of a given profile, and the determination of the profile shape necessary to yield a given pressure distribution for small chord gap ratios, For incompressible flow the results of the theory are compared with available examples obtained by the more exact method of conformal transformation. Although the theory is developed for small chord/gap ratios, these comparisons show that it may be extended to chord/gap ratios of order unity, at least for low speed flows. Choking of cascades, a phenomenon of particular importance in compressor design, is considered.
A theory of unstaggered airfoil cascades in compressible flow
By use of the methods of thin airfoil theory, which include effects of compressibility, relations are developed which permit the rapid determination of the pressure distribution over an unstaggered cascade of airfoils of a given profile, and the determination of the profile shape necessary to yield a given pressure distribution for small chord/gap ratios. For incompressible flow the results of the theory are compared with available examples obtained by the more exact method of conformal transformation. Although the theory is developed for small chord/gap ratios, these comparisons show that it may be extended to chord/gap ratios of order unity, at least for low-speed flows. Choking cascades, a phenomenon of particular importance in compressor design, is considered.
The theory of wind-tunnel wall interference
This report outlines the development of a general theory for the calculation of the effect of the boundaries of the air stream on the flow past an airfoil. Analytical treatments are given for tunnels with horizontal boundaries only, with vertical boundaries only, and with a bottom boundary only. Formulas are developed for the tunnel wall interference in each case for an airfoil located at the center of the tunnel. The correction is given as a function of the width to height ratio of the tunnel. The formulas are exact for infinitely small airfoils only, but give good approximation for spans up to about three-quarters of the tunnel width.
Theory of Wing-Body Drag at Supersonic Speeds
At subsonic speeds the pressure drag arising from the thickness of the body or wings is negligible so long as the shapes are sufficiently well streamlined to avoid flow separation. In that range there exists no possibility of either favorable or adverse interference on the pressure distributions themselves. If one body is so placed as to receive a drag from the pressure field of another then the second body is sure to receive a corresponding increment of thrust from the first. At supersonic speeds this tolerance, which was permitted the designer, disappears and the drag becomes sensitive to the shape and arrangement of the bodies.To be sure, the primary factor here is the thickness ratio, but nevertheless there exist arrangements in which a large cancellation of drag occurs.
Theory of wing-body drag at supersonic speeds
The relation of Whitcomb's "area rule" to the linear formulas for wave drag at lightly supersonic speeds is discussed. By adopting an approximate relation between the source strength and the geometry of a wing-body combination, the wave-drag theory is expressed in terms involving the areas intercepted by oblique planes or Mach planes. The resulting formulas are checked by comparison with the drag measurements obtained in wind-tunnel experiments and in experiments with falling models in free air. Finally, a theory for determining wing-body shapes of minimum drag at supersonic Mach numbers is discussed and some preliminary experiments are reported.
Theory of wing sections of arbitrary shape
This report presents a solution of the problem of the theoretical flow of a frictionless incompressible fluid past airfoils of arbitrary forms. The velocity of the 2-dimensional flow is explicitly expressed for any point of the surface, and for any orientation, by an exact expression containing a number of parameters which are functions of the form only and which may be evaluated by convenient graphical methods. The method is particularly simple and convenient for bodies of streamline forms. The results have been applied to typical airfoils and compared with experimental data.
Theory of Wings in Nonstationary Flow
This paper gives an overview of equations for vibration and flutter affecting airplane wings in nonstationary flow.
Thermal analysis of sodium hydroxide containing the reaction products of sodium hydroxide and chromium metal
Cooling curves were established for melts of sodium hydroxide that had been reacted with up to 20-percent-by-weight additions of chromium metal for varying times at 820 degrees C (1500 degrees F). For any given time at temperature, the depression of the freezing point of the hydroxide was increased with increasing chromium concentration. This depression diminished with increasing reaction time. A eutectic of the hydroxide and some reaction product was observed at 289 degrees plus or minus 3 degrees C. This eutectic was not evident at low chromium concentrations and disappeared at long reaction times.