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

**Collection:**National Advisory Committee for Aeronautics Collection

### The physical effects of detonation in a closed cylindrical chamber

**Date:**January 1, 1935

**Creator:**Draper, C S

**Description:**Detonation in the internal-combustion engine is studied as a physical process. It is shown that detonation is accompanied by pressure waves within the cylinder charge. Sound theory is applied to the calculation of resonant pressure-wave frequencies. Apparatus is described for direct measurement of pressure-wave frequencies. Frequencies determined from two engines of different cylinder sizes are shown to agree with the values calculated from sound theory. An outline of the theoretically possible modes of vibration in a right circular cylinder with flat ends is included. An appendix by John P. Elting gives a method of calculating pressure in the sound wave following detonation.

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### General airplane performance

**Date:**January 1, 1939

**Creator:**Rockfeller, W C

**Description:**Equations have been developed for the analysis of the performance of the ideal airplane, leading to an approximate physical interpretation of the performance problem. The basic sea-level airplane parameters have been generalized to altitude parameters and a new parameter has been introduced and physically interpreted. The performance analysis for actual airplanes has been obtained in terms of the equivalent ideal airplane in order that the charts developed for use in practical calculations will for the most part apply to any type of engine-propeller combination and system of control, the only additional material required consisting of the actual engine and propeller curves for propulsion unit. Finally, a more exact method for the calculation of the climb characteristics for the constant-speed controllable propeller is presented in the appendix.

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### Elastic instability of members having sections common in aircraft construction

**Date:**January 1, 1932

**Creator:**Trayer, George W & March, H W

**Description:**Two fundamental problems of elastic stability are discussed in this report. In part one formulas are given for calculating the critical stress at which a thin, outstanding flange of a compression member will either wrinkle into several waves or form into a single half wave and twist the member about its longitudinal axis. A mathematical study of the problem, which together with experimental work has led to these formulas, is given in an appendix. Results of test substantiating the recommended formulas are also presented. In part two the lateral buckling of beams is discussed. The results of a number of mathematical studies of this phenomenon have been published prior to this writing, but very little experimentally determined information relating to the problem has been available heretofore. Experimental verification of the mathematical deductions is supplied.

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### Air propellers in yaw

**Date:**January 1, 1937

**Creator:**Lesley, E P; Worley, George F & Moy, Stanley

**Description:**Report presents the results of tests conducted at Stanford University of a 3-foot model propeller at four pitch settings and at 0 degree, 10 degrees, 20 degrees, and 30 degrees yaw. In addition to the usual propeller coefficients, cross-wind and vertical forces and yawing, pitching, and rolling moments were determined about axes having their origin at the intersection of the blade axis and the axis of rotation. The tests showed that the maximum efficiency was reduced only slightly for angles of yaw up to 10 degrees but that at 30 degrees yaw the loss in efficiency was about 10 percent. In all cases the cross-wind force was found to be greater than the cross-wind component of the axial thrust. With a yawed propeller an appreciable thrust was found for v/nd for zero thrust at zero yaw. Yawing a propeller was found to induce a pitching moment that increased in magnitude with yaw.

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### Application of practical hydrodynamics to airship design

**Date:**January 1, 1933

**Creator:**Upson, Ralph H & Klikoff, W A

**Description:**The purpose of the first two parts of this report is to present in concise format all the formulas required for computation of the hydrodynamic forces, so that they can be easily computed for either straight or curvilinear flight. Improved approximations are also introduced having a high degree of accuracy throughout the entire range of practical proportions. The remaining two parts of the report are devoted respectively to stability and skin friction, as functions of the same hydrodynamic forces.

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### A proof of the theorem regarding the distribution of lift over the span for minimum induced drag

**Date:**January 1, 1931

**Creator:**Durand, W F

**Description:**The proof of the theorem that the elliptical distribution of lift over the span is that which will give rise to the minimum induced drag has been given in a variety of ways, generally speaking too difficult to be readily followed by the graduate of the average good technical school of the present day. In the form of proof this report makes an effort to bring the matter more readily within the grasp of this class of readers.

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### Aircraft woods: their properties, selection, and characteristics

**Date:**January 1, 1931

**Creator:**Markwardt, L J

**Description:**Strength values of various woods for aircraft design for a 15 per cent moisture condition of material and a 3-second duration of stress are presented, and also a discussion of the various factors affecting the values. The toughness-test method of selecting wood is discussed, and a table of acceptance values for several species is given.

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### A method of calculating the ultimate strength of continuous beams

**Date:**January 1, 1931

**Creator:**Newlin, J A & Trayer, George W

**Description:**The purpose of this study was to investigate the strength of continuous beams after the elastic limit has been passed. As a result, a method of calculation, which is applicable to maximum load conditions, has been developed. The method is simpler than the methods now in use and it applies properly to conditions where the present methods fail to apply.

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### Stability of thin-walled tubes under torsion

**Date:**January 1, 1935

**Creator:**Donnell, L H

**Description:**In this report a theoretical solution is developed for the torsion on a round thin-walled tube for which the walls become unstable. The results of this theory are given by a few simple formulas and curves which cover all cases. The differential equations of equilibrium are derived in a simpler form than previously found, it being shown that many items can be neglected.

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### An extended theory of thin airfoils and its application to the biplane problem

**Date:**January 1, 1931

**Creator:**Millikan, Clark B

**Description:**The report presents a new treatment, due essentially to von Karman, of the problem of the thin airfoil. The standard formulae for the angle of zero lift and zero moment are first developed and the analysis is then extended to give the effect of disturbing or interference velocities, corresponding to an arbitrary potential flow, which are superimposed on a normal rectilinear flow over the airfoil. An approximate method is presented for obtaining the velocities induced by a 2-dimensional airfoil at a point some distance away. In certain cases this method has considerable advantage over the simple "lifting line" procedure usually adopted. The interference effects for a 2-dimensional biplane are considered in the light of the previous analysis. The results of the earlier sections are then applied to the general problem of the interference effects for a 3-dimensional biplane, and formulae and charts are given which permit the characteristics of the individual wings of an arbitrary biplane without sweepback or dihedral to be calculated. In the final section the conclusions drawn from the application of the theory to a considerable number of special cases are discussed, and curves are given illustrating certain of these conclusions and serving as examples to indicate ...

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### Investigation of turbulent flow in a two-dimensional channel

**Date:**January 1, 1951

**Creator:**Laufer, John

**Description:**A detailed exploration of the field of mean and fluctuating quantities in a two-dimensional turbulent channel flow is presented. The measurements were repeated at three Reynolds numbers, 12,300, 30,800, and 61,600, based on the half width of the channel and the maximum mean velocity. A channel of 5-inch width and 12:1 aspect ratio was used for the investigation. Mean-speed and axial-fluctuation measurements were made well within the laminar sublayer. The semitheoretical predictions concerning the extent of the laminar sublayer were confirmed. The distribution of the velocity fluctuations in the direction of mean flow u' shows that the influence of the viscosity extends farther from the wall than indicated by the mean velocity profile, the region of influence being approximately four times as wide.

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### On the theory of oscillating airfoils of finite span in subsonic compressible flow

**Date:**January 1, 1950

**Creator:**Reissner, Eric

**Description:**The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

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### A special investigation to develop a general method for three-dimensional photoelastic stress analysis

**Date:**January 1, 1953

**Creator:**Frocht, M M & Guernsey, R , Jr

**Description:**The method of strain measurement after annealing is reviewed and found to be satisfactory for the materials available in this country. A new general method is described for the photoelastic determination of the principal stresses at any point of a general body subjected to arbitrary load. The method has been applied to a sphere subjected to diametrical compressive loads. The results show possibilities of high accuracy.

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### An experimental investigation of transonic flow past two-dimensional wedge and circular-arc sections using a Mach-Zehnder interferometer

**Date:**January 1, 1952

**Creator:**Bryson, Arthur Earl, Jr

**Description:**Report presents the results of interferometer measurements of the flow field near two-dimensional wedge and circular-arc sections of zero angle of attack at high-subsonic and low-supersonic velocities. Both subsonic flow with local supersonic zone and supersonic flow with detached shock wave have been investigated. Pressure distributions and drag coefficients as a function of Mach number have been obtained. The wedge data are compared with the theoretical work on flow past wedge sections of Guderley and Yoshihara, Vincenti and Wagner, and Cole. Pressure distributions and drag coefficients for the wedge and circular-arc sections are presented throughout the entire transonic range of velocities.

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### Analysis and calculation by integral methods of laminar compressible boundary-layer with heat transfer and with and without pressure gradient

**Date:**January 1, 1955

**Creator:**Morduchow, Morris

**Description:**A survey of integral methods in laminar-boundary-layer analysis is first given. A simple and sufficiently accurate method for practical purposes of calculating the properties (including stability) of the laminar compressible boundary layer in an axial pressure gradient with heat transfer at the wall is presented. For flow over a flat plate, the method is applicable for an arbitrarily prescribed distribution of temperature along the surface and for any given constant Prandtl number close to unity. For flow in a pressure gradient, the method is based on a Prandtl number of unity and a uniform wall temperature. A simple and accurate method of determining the separation point in a compressible flow with an adverse pressure gradient over a surface at a given uniform wall temperature is developed. The analysis is based on an extension of the Karman-Pohlhausen method to the momentum and the thermal energy equations in conjunction with fourth- and especially higher degree velocity and stagnation-enthalpy profiles.

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### Diffusion of heat from a line source in isotropic turbulence

**Date:**January 1, 1953

**Creator:**Uberoi, Mahinder S & Corrsin, Stanley

**Description:**An experimental and analytical study has been made of some features of the turbulent heat diffusion behind a line heated wire stretched perpendicular to a flowing isotropic turbulence. The mean temperature distributions have been measured with systematic variations in wind speed, size of turbulence-producing grid, and downstream location of heat source. The nature of the temperature fluctuation field has been studied. A comparison of Lagrangian and Eulerian analyses for diffusion in a nondecaying turbulence yields an expression for turbulent-heat-transfer coefficient in terms of turbulence velocity and a Lagrangian "scale." the ratio of Eulerian to Lagrangian microscale has been determined theoretically by generalization of a result of Heisenberg and with arbitrary constants taken from independent sources, shows rough agreement with experimental results. A convenient form has been deduced for the criterion of interchangeability of instantaneous space and time derivatives in a flowing turbulence.

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### Free-stream boundaries of turbulent flows

**Date:**January 1, 1955

**Creator:**Corrsin, Stanley & Kistler, Alan L

**Description:**Report presents the results of an experimental and theoretical study made of the instantaneously sharp and irregular front which is always found to separate turbulent fluid from contiguous "nonturbulent" fluid at a free-stream boundary. This distinct demarcation is known to give an intermittent character to hot-wire signals in the boundary zone. The overall behavior of the front is described statistically in terms of its wrinkle-amplitude growth and its lateral propagation relative to the fluid as functions of downstream coordinate.

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### Experiments to determine neighborhood reactions to light airplanes with and without external noise reduction

**Date:**January 1, 1953

**Creator:**Elwell, Fred S

**Description:**The work reported was part of a program of experimentation with external noise reduction on light airplanes. This particular study was in effect a byproduct survey conceived to utilize already available equipment and personnel to further the findings of the original research and to determine reactions in populated neighborhoods to light aircraft with and without noise-reduction equipment. The findings indicate that at the 10 sites within and about metropolitan Boston the degree of noise reduction previously found to be aerodynamically and structurally feasible did eliminate substantially all neighborhood objections to noise per se. The evidence clearly suggests that, when the noise nuisance is minimized to the extent found feasible, the number and severity of other objections also diminish -- evidently because the flight operations are noticed less when heard less.

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### Experimental aerodynamic derivatives of a sinusoidally oscillating airfoil in two-dimensional flow

**Date:**January 1, 1952

**Creator:**Halfman, Robert L

**Description:**Experimental measurements of the aerodynamic reactions on a symmetrical airfoil oscillating harmonically in a two-dimensional flow are presented and analyzed. Harmonic motions include pure pitch and pure translation, for several amplitudes and superimposed on an initial angle of attack, as well as combined pitch and translation. The apparatus and testing program are described briefly and the necessary theoretical background is presented. In general, the experimental results agree remarkably well with the theory, especially in the case of the pure motions. The net work per cycle for a motion corresponding to flutter is experimentally determined to be zero. Considerable consistent data for pure pitch were obtained from a search of available reference material, and several definite Reynolds number effects are evident.

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### Recommendations for numerical solution of reinforced-panel and fuselage-ring problems

**Date:**January 1, 1949

**Creator:**Hoff, N J & Libby, Paul A

**Description:**Procedures are recommended for solving the equations of equilibrium of reinforced panels and isolated fuselage rings as represented by the external loads and the operations table established according to Southwell's method. From the solution of these equations the stress distribution can be easily determined. The method of systematic relaxations, the matrix-calculus method, and several other methods applicable in special cases are discussed. Definite recommendations are made for obtaining the solution of reinforced-panel problems which are generally designated as shear lag problems. The procedures recommended are demonstrated in the analysis of a number of panels. In the case of fuselage rings it is not possible to make definite recommendations for the solution of the equilibrium equations for all rings and loadings. However, suggestions based on the latest experience are made and demonstrated on several rings.

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### On the development of turbulent wakes from vortex streets

**Date:**January 1, 1954

**Creator:**Roshko, Anatol

**Description:**Wake development behind circular cylinders at Reynolds numbers from 40 to 10,000 was investigated in a low-speed wind tunnel. Standard hot-wire techniques were used to study the velocity fluctuations. The Reynolds number range of periodic vortex shedding is divided into two distinct subranges. At r=40 to 150, called the stable range, regular vortex streets are formed and no turbulent velocity fluctuations accompany the periodic formation of vortices. The range r=150 to 300 is a transition range to a regime called the irregular range, in which turbulent velocity fluctuations accompany the periodic formation of vortices. The turbulence is initiated by laminar-turbulent transition in the free layers which spring from the separation points on the cylinder. The transition first occurs in the range r=150 to 300. Spectrum and statistical measurements were made to study the velocity fluctuations.

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### Influence of Alloying upon Grain-Boundary Creep

**Date:**January 1, 1957

**Creator:**Rhines, F N; Bond, W E & Kissel, M A

**Description:**Grain-boundary displacement, occurring in bicrystals during creep at elevated temperature (350 degrees c), has been measured as a function of the copper content (0.1 to 3 percent) in a series of aluminum-rich aluminum-copper solid-solution alloys. The minimums in stress and temperature, below which grain-boundary motion does not occur, increase regularly with the copper content as would be expected if recovery is necessary for movement. Otherwise, the effects, if any, of the copper solute upon grain-boundary displacement and its rate are too small for identification by the experimental technique employed. It was shown, additionally, that grain-boundary displacement appears regular and proceeds at a constant rate if observed parallel to the stress axis, whereas the motion is seen to occur in a sequence of surges and the rate to diminish with time if the observations are made perpendicular to the stress axis.

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### Development of turbulence-measuring equipment

**Date:**January 1, 1954

**Creator:**Kovasznay, Leslie S G

**Description:**Hot wire turbulence-measuring equipment has been developed to meet the more stringent requirements involved in the measurement of fluctuations in flow parameters at supersonic velocities. The higher mean speed necessitates the resolution of higher frequency components than at low speed, and the relatively low turbulence level present at supersonic speed makes necessary an improved noise level for the equipment. The equipment covers the frequency range from 2 to about 70,000 cycles per second. Constant-current operation is employed. Compensation for hot-wire lag is adjusted manually using square-wave testing to indicate proper setting. These and other features make the equipment adaptable to all-purpose turbulence work with improved utility and accuracy over that of older types of equipment. Sample measurements are given to demonstrate the performance.

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### Direct measurements of skin friction

**Date:**January 1, 1953

**Creator:**Dhawan, Satish

**Description:**A device has been developed to measure local skin friction on a flat plate by measuring the force exerted upon a very small movable part of the surface of the flat plate. These forces, which range from about 1 milligram to about 100 milligrams, are measured by means of a reactance device. The apparatus was first applied to measurements in the low-speed range, both for laminar and turbulent boundary layers. The measured skin-friction coefficients show excellent agreement with Blasius' and Von Karman's results. The device was then applied to high-speed subsonic flow and the turbulent-skin-friction coefficients were determined up to a Mach number of about 0.8. A few measurements in supersonic flow were also made. This paper describes the design and construction of the device and the results of the measurements.

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