# Search Results

Analytical Treatment of Normal Condensation Shock
The condensation of water vapor in an air consequences: acquisition of heat (liberated heat vaporization; loss of mass on the part of the flowing gas (water vapor is converted to liquid); change in the specific gas constants and of the ratio k of the specific heats (caused by change of gas composition). A discontinuous change of state is therefore connected with the condensation; schlieren photographs of supersonic flows in two-dimensional Laval nozzles show two intersecting oblique shock fronts that in the case of high humidities may merge near the point of intersection into one normal shock front.
The Calculation of Compressible Flows with Local Regions of Supersonic Velocity
This report addresses a method for the approximate calculation of compressible flows about profiles with local regions of supersonic velocity. The flow around a slender profile is treated as an example.
Calculation of the Pressure Distribution on Bodies of Revolution in the Subsonic Flow of a Gas, Part 1, Axially Symmetrical Flow
The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.
Calculations and Experimental Investigations on the Feed-Power Requirement of Airplanes with Boundary-Layer Control
Calculations and test results are given about the feed-power requirement of airplanes with boundary-layer control. Curves and formulas for the rough estimate of pressure-loss and feed-power requirement are set up for the investigated arrangements which differ structurally and aerodynamically. According to these results the feed power for three different designs is calculated at the end of the report.
Calibration and Measurement in Turbulence Research by the Hot-Wire Method
The problem of turbulence in aerodynamics is at present being attacked both theoretically and experimentally. In view of the fact however that purely theoretical considerations have not thus far led to satisfactory results the experimental treatment of the problem is of great importance. Among the different measuring procedures the hot wire methods are so far recognized as the most suitable for investigating the turbulence structure. The several disadvantages of these methods however, in particular those arising from the temperature lag of the wire can greatly impair the measurements and may easily render questionable the entire value of the experiment. The name turbulence is applied to that flow condition in which at any point of the stream the magnitude and direction of the velocity fluctuate arbitrarily about a well definable mean value. This fluctuation imparts a certain whirling characteristic to the flow.
Coefficient of Friction, Oil Flow and Heat Balance of a Full-Journal Bearing
No Description Available.
The Combination of Internal-Combustion Engine and Gas Turbine
While the gas turbine by itself has been applied in particular cases for power generation and is in a state of promising development in this field, it has already met with considerable success in two cases when used as an exhaust turbine in connection with a centrifugal compressor, namely, in the supercharging of combustion engines and in the Velox process, which is of particular application for furnaces. In the present paper the most important possibilities of combining a combustion engine with a gas turbine are considered. These "combination engines " are compared with the simple gas turbine on whose state of development a brief review will first be given. The critical evaluation of the possibilities of development and fields of application of the various combustion engine systems, wherever it is not clearly expressed in the publications referred to, represents the opinion of the author. The state of development of the internal-combustion engine is in its main features generally known. It is used predominantly at the present time for the propulsion of aircraft and road vehicles and, except for certain restrictions due to war conditions, has been used to an increasing extent in ships and rail cars and in some fields applied as stationary power generators. In the Diesel engine a most economical heat engine with a useful efficiency of about 40 percent exists and in the Otto aircraft engine a heat engine of greatest power per unit weight of about 0.5 kilogram per horsepower.
Compression Shocks of Detached Flow
It is known that compression shocks which lead from supersonic to subsonic velocity cause the flow to separate on impact on a rigid wall. Such shocks appear at bodies with circular symmetry or wing profiles on locally exceeding sonic velocity, and in Laval nozzles with too high a back pressure. The form of the compression shocks observed therein is investigated.
Concerning the Velocity of Evaporation of Small Droplets in a Gas Atmosphere
The evaporation velocity of liquid droplets under various conditions is theoretically calculated and a number of factors are investigated which are neglected in carrying out the fundamental equation of Maxwell. It is shown that the effect of these factors at the small drop sizes and the small weight concentrations ordinarily occurring in fog can be calculated by simple corrections. The evaporation process can be regarded as quasi-stationary in most cases. The question at hand, and also the equivalent question of the velocity of growth of droplets in a supersaturated atmosphere, is highly significant in meteorology and for certain industrial purposes. Since the literature concerning this is very insufficient and many important aspects either are not considered at all or are reported incorrectly, it seems that a short discussion is not superfluous. A special consideration will be given to the various assumptions and neglections that are necessary in deriving the fundamental equation of Maxwell. The experimental work available, which is very insufficient and in part poorly dependable, can be used as an accurate check on the theory only in very few cases.
Cones in Supersonic Flow
In the case of cones in axially symmetric flow of supersonic velocity, adiabatic compression takes place between shock wave and surface of the cone. Interpolation curves betwen shock polars and the surface are therefore necessary for the complete understanding of this type of flow. They are given in the present report by graphical-numerical integration of the differential equation for all cone angles and airspeeds.
Description of Russian Aircraft Engines "AM 35" and "AM 38"
The Russian AM 35 and AM 38 aircraft engines have superchargers with a swirl throttle, which appears to be a purely Russian development. This paper gives the results of test runs of the two engines, including the effects of the swirl throttle on engine performance.
Determination of the Stress Concentration Factor of a Stepped Shaft Stressed in Torsion by Means of Precision Strain Gages
The stress distribution in stepped shafts stressed in torsion is determined by means of the electric precision strain gage the stress concentration factor is ascertained from the measurements. It is shown that the test values always are slightly lower than the values resulting from an approximate formula.
Development and Construction of an Interferometer for Optical Measurements of Density Fields
A method of interference is described in the present report which promises profitable application in aeronautical research. The physical foundation of the method and a simple method of adjustment are briefly discussed. The special technical construction of the instrument is described which guarantees its use also in the case of vibrations of the surrounding space and permits the investigation of unsteady phenomena. It is found that the interference method will make the small differences in density in the flow field around the body even at low speeds. (40 m/sec) optically measurable.
The Distribution of Loads on Rivets Connecting a Plate to a Beam under Transverse Loads
This report gives theoretical discussion of the distribution of leads on rivets connecting a plate to a beam under transverse leads. Two methods of solution are given which are applicable to loads up to the limit of proportionality; in the first the rivets are treated as discrete members, and in the second they are replaced by a continuous system of jointing. A method of solution is also given which is applicable to the case when nonlinear deformations occur in the rivets and the plate, but not in the beam. The methods are illustrated by numerical examples, and these show that the loads carried by the rivets and the plate are less than the values given by classical theory, which does not take into account the slip of the rivets, even below the limit of proportionality. The difference is considerably accentuated when nonlinear deformations occur in the restructure and the beam then carries the greater portion of the bending moment. If the material of the beam has a higher proportional limit and a higher ultimate strength than the material of the plate, there is thus a transfer of load from weaker to stronger material, and this is to the advantage of the structure. The methods given are of simple application and are recommended for use in the design of light-alloy structures when the design lead is likely to be above the proportional limit.
Drag Corrections in High-Speed Wind Tunnels
In the vicinity of a body in a wind tunnel the displacement effect of the wake, due to the finite dimensions of the stream, produces a pressure gradient which evokes a change of drag. In incompressible flow this change of drag is so small, in general, that one does not have to take it into account in wind-tunnel measurements; however, in compressible flow it beoomes considerably larger, so that a correction factor is necessary for measured values. Correction factors for a closed tunnel and an open jet with circular cross sections are calculated and compared with the drag - corrections already bown for high-speed tunnnels.
Drag Reduction by Suction of the Boundary Layer Separated Behind Shock Wave Formation at High Mach Numbers
With an approach of the velocity of flight of a ship to the velocity of sound, there occurs a considerable increase of the drag. The reason for this must be found in the boundary layer separation caused by formation of shock waves. It will be endeavored to reduce the drag increase by suction of the boundary layer. Experimental results showed that drag increase may be considerably reduced by this method. It was, also, observed that, by suction, the position of shock waves can be altered to a considerable extent.
The Effect of Turbulence on the Flame Velocity in Gas Mixtures
The present report deals with the effect of turbulence on the propagation of the flame. Being based upon experiments with laminar as well as turbulent Bunsen flames, both the physico-chemical and the hydro-dynamical aspects of the problem are analyzed. A number of new deductions, interesting from the point of view of engine combustion and other very rapidly changing flame reactions, are made.
The Elasto-Plastic Stability of Plates
This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.
This paper makes the following assumptions: 1) The flowing gases are assumed to have uniform energy distribution. ("Isoenergetic gas flows," that is valid with the same constants for the the energy equation entire flow.) This is correct, for example, for gas flows issuing from a region of constant pressure, density, temperature, end velocity. This property is not destroyed by compression shocks because of the universal validity of the energy law. 2) The gas behaves adiabatically, not during the compression shock itself but both before and after the shock. However, the adiabatic equation (p/rho(sup kappa) = C) is not valid for the entire gas flow with the same constant C but rather with an appropriate individual constant for each portion of the gas. For steady flows, this means that the constant C of the adiabatic equation is a function of the stream function. Consequently, a gas that has been flowing "isentropically",that is, with the same constant C of the adiabatic equation throughout (for example, in origination from a region of constant density, temperature, and velocity) no longer remains isentropic after a compression shock if the compression shock is not extremely simple (wedge shaped in a two-dimensional flow or cone shaped in a rotationally symmetrical flow). The solution of nonisentropic flows is therefore an urgent necessity.
A calulation of the flow in turbine blading is reported that includes the calculation of effect of centrifugal force. Frictional losses on the stator blades and rotor blades are allowed.
Force and pressure-distribution measurements on a rectangular wing with a slotted droop nose and with either plain and split flaps in combination or a slotted flap.
Force measurements and pressure distribution measurements on the midsection were made on a rectangular wing with slotted droop nose and end plates, on which could be placed a choice of either a plain flap-split flap combination or a slotted flap. (author).
Force and Pressure-Distribution Measurements on a Rectangular Wing with Double-Hinged Nose
The previous measurements on airfoils with hinged nose disclosed a comparatively large low-pressure peak at the bend of the hinged nose; which favored the separation of flow. It was therefore attempted to reduce these low-pressure peaks by reducing the camber of the forward profile and thereby ensure a longer adherence of the flow and a maximum lift increase. The forces were measured on a rectangular wing with double-hinged nose and end plates, the pressure distributions were measured in the center section of the wing. The measurements disclosed that the highest lift attained with a single-hinged nose cannot be increased by a double-hinged nose. The sum of the deflection angles of both hinged noses related to the maximum lift is about equal to the corresponding angle of the single-hinge nose (approx. 30 deg to 40). The respective angle of attack in both cases amounts to approx. 21 deg. Even the low-pressure peak is about the same in both cases (P/q approx. -5.5). Therefore, a milder curvature of the forward portion of the profile affords no definite increase of the maximum lift.
Fundamental Aerodynamic Investigations for Development of Arrow-Stabilized Projectiles
The numerous patent applications on arrow-stabilized projectiles indicate that the idea of projectiles without spin is not new, but has appeared in various proposals throughout the last decades. As far as projectiles for subsonic speeds are concerned, suitable shapes have been developed for sometime, for example, numerous grenades. Most of the patent applications, though, are not practicable particularly for projectiles with supersonic speed. This is because the inventor usually does not have any knowledge of aerodynamic flow around the projectile nor any particular understanding of the practical solution. The lack of wind tunnels for the development of projectiles made it necessary to use firing tests for development. These are obviously extremely tedious or expensive and lead almost always to failures. The often expressed opinion that arrow-stabilized projectiles cannot fly supersonically can be traced to this condition. That this is not the case has been shown for the first time by Roechling on long projectiles with foldable fins. Since no aerodynamic investigations were made for the development of these projectiles, only tedious series of firing tests with systematic variation of the fins could lead to satisfactory results. These particular projectiles though have a disadvantage which lies in the nature cf foldable fins. They occasionally do not open uniformly in flight, thus causing unsymmetry in flow and greater scatter. The junctions of fins and body are very bad aerodynamically and increase the drag. It must be possible to develop high-performance arrow-stabilized projectiles based on the aerodynamic research conducted during the last few years at Peenemuende and new construction ideas. Thus the final shape, ready for operational use, could be developed in the wind tunnel without loss of expensive time in firing tests. The principle of arrow-stabilized performance has been applied to a large number of caliburs which were stabilized by various means ...
Fundamentals of the Control of Gas-Turbine Power Plants for Aircraft, Part 1, Standardization of the Computations Relating to the Control of Gas-Turbine Power Plants for Aircraft by the Employment of the Laws of Similarity
It will be shown that by the use of the concept of similarity a simple representation of the characteristic curves of a compressor operating in combination with a turbine may be obtained with correct allowance for the effect of temperature. Furthermore, it bec~mes possible to simplify considerably the rather tedious investigations of the behavior of gas-turbine power plants under different operating conditions. Characteristic values will be derived for the most important elements of operating behavior of the power plant, which will be independent of the absolute valu:s of pressure and temperature. At the same time, the investigations provide the basis for scale-model tests on compressors and turbines.
Fundamentals of the Control of Gas-Turbine Power Plants for Aircraft, Part 2, Principles of Control Common to Jet, Turbine-Propeller Jet, and Ducted-Fan Jet Power Plants
After defining the aims and requirements to be set for a control system of gas-turbine power plants for aircraft, the report will deal with devices that prevent the quantity of fuel supplied per unit of time from exceeding the value permissible at a given moment. The general principles of the actuation of the adjustable parts of the power plant are also discussed.
Fundamentals of the Control of Gas-Turbine Power Plants for Aircraft. Part III Control of Jet Engines, Part 3, Control of Jet Engines
The basic principles of the control of TL ongincs are developed on .the basis of a quantitative investigation of the behavior of these behavior under various operating conditions with particular consideration of the simplifications pormissible in each case. Various possible means of control of jet engines are suggested and are illustrated by schematic designs.
Gas-Dynamic Investigations of the Pulse-Jet Tube, Parts 1 and 2
Based upon a simplified representation of the mode of operation of the pulse-jet tube, the effect of the influences mentioned in the title were investigated and it will be shown that, for a jet tube with a fccmndesigned to be aerodynamically favorable, the ability to operate is at least questionable. By taking into account the course of the development of pressure by combustion, a new insight has been obtained into the processes of motion within the jet tube, an insight that explains a number of empirical observations, namely: certain particulars of the sequence of pressure variations; the existence of an optimum valve-opening ratio; the occurrence of an intrusion of air; and the existence of a flight speed above lrhichthe jet tube ceases to operate. At too great an opening ratio or at too great a flight s-peed, the continuous flow through the tube is too predominant over the oscilla~ory process to perinitthe occurrence of an explosion powerful enough to maintain continuous operation. Certain possible means of making the operation of the jet tube more independent of the flight speed and of reducing the flow losses were proposed and discussed.
Gas-Dynamic Investigations of the Pulse-Jet Tube, Parts 1 and 2
Based upon a simplified representation of the mode of operation of the pulse-jet tube, the effect of the influences mentioned in the title were investigated and it will be shown that, for a jet tube with a form designed to be aerodynamically favorable, the ability to operate is at least questionable. This investigation will account for the important practical observation made by Paul Schmidt that the ratio of the effective valve cross-sectional area to the tube cross section may not be of any random magnitude and will explain why at too great flight speeds the jet tube ceases to operate. Chemical an thermodynamic processes (for example, constituents or mode of fuel-air-mixture formation or heat losses) are unimportant in this regard.
General Characteristics of the Flow through Nozzles at Near Critical Speeds
The characteristics of the position and form of the transition surface through the critical velocity are computed for flow through flat and round nozzles from subsonic to supersonic velocity. Corresponding considerations were carried out for the flow about profiles in the vicinity of sonic velocity.
High-Speed Measurements on a Swept-Back Wing (Sweepback Angle phi = 35 Deg)
In the following, high-speed measurements on a swept-back wing are reported. The curves of lift, moment, and drag have been determined up to Mach numbers of M = 0.87, and they are compared to a rectangular wing. Through measurements of the total-head loss behind the wing and through schlieren pictures, an insight into the formation of the compression shock at high Mach numbers has been obtained.
Infinitesimal Conical Supersonic Flow
The calculation of infinitesimal conical supersonic flow has been applied first to the simplest examples that have also been calculated in another way. Except for the discovery of a miscalculation in an older report, there was found the expected conformity. The new method of calculation is limited more definitely to the conical case.
Investigation of the Operating Properties of the Leakage Current Anemometer
Freedom from inertia, erosion of electrodes, and reaction make the leakage current particularly appropriate for the measurement of flow velocities in gases. Apparatus previously described has now been improved by reducing the size of the electrodes by one -thousandth, as is necessary aerodynamically, and by increasing the magnitude of the current from 1000 to 10,000 times; the latter result was obtained.by use of mercury high-pressure lamps set up at the one focal point of an ellipsoidal reflector with the cathodes arranged at the other focal point or by use of suitable X-ray radiation. Families of calibration curves were taken with a number of vivid tests conditions of the greatest variety and the operating properties of the instrument were widely elucidated by calculation of the sensitivity to fluctuation; this was done at first for operation at stationary conditions only; due to the freedom from inertia the instationary conditions were thus also given. Accordingly, the leakage current anemometer ought to be appropriate for investigations of turbulence,.
Investigations of Compression Shocks and Boundary Layers in Gases Moving at High Speed
The mutual influences of compression shocks and friction boundary layers were investigated by means of high speed wind tunnels.Schlieren optics provided a clear picture of the flow phenomena and were used for determining the location of the compression shocks, measurement of shock angles, and also for Mach angles. Pressure measurement and humidity measurements were also taken into consideration.Results along with a mathematical model are described.
Investigations on Experimental Impellers for Axial Blowers
A selection of measurements obtained on experimental impellers for axial blowers will be reported. In addition to characteristic curves plotted for low and for high peripheral velocities, proportions and blade sections for six different blower models and remarks on the design of blowers will be presented.
Investigations on Reductions of Friction on Wings, in Particular by Means of Boundary Layer Suction
Memorandum presenting investigation on reductions of friction on wings, especially by means of boundary-layer suction. The report is broken up into several sections, including: causes of transition, laminar profiles with the transition taking place, laminar boundary-layer suction, investigation of the laminar pressure increase, investigation of the slot flow for laminar boundary-layer suction with single slots, tests about keeping a boundary layer for high Reynolds laminar with the aid of boundary-layer suction, and an investigation of a slightly-cambered laminar suction profile of 10.5-percent thickness.
Laboratory Report on the Investigation of the Flow around Two Turbine-Blade Profiles using the Interferometer Method
At the request of the Junkers Aircraft and Engine Construction Company, Engine Division, Dessau Main Plant, an investigation was made using the interferometer method on the two turbine-blade profiles submitted. The interferometer method enables making visible the differences in density and consequently the boundary layers that develop when a flow is directed on the profile. Recognition of the points on the profile at which separation of flow occurs is thus possible. By means of the interference photographs the extent of the dead-water region may be ascertained. The size of the dead-water region provides evidence as to the quality of the flow and allows a qualitative estimate of the amount of the flow losses. Interference photographs thus provide means of judging the utility of profiles under specific operating conditions and provide suggestions for possible changes of profile contours that might help to improve flow relations. Conclusions may be drawn concerning the influence of the blade-spacing ratio, the inlet-air angle, and the connection between the curvature of the profile contour and the point of separation of the flow from the profile surface.
Lift and Drag of Wings with Small Span
The lift coefficient of a wing of small span at first shows a linear increase for the increasing angle of attack, but to a lesser degree then was to be expected according to the theory of the lifting line; thereafter the lift coefficient increases more rapidly than linearity, as contrasted with the the theory of the lifting line. The induced drag coefficient for a given lift coefficient, on the other hand, is obviously much smaller than it would be according to the theory. A mall change in the theory of the lifting line will cover these deviations.
The Lift Distribution of Swept-Back Wings
Two procedures for calculating the lift distribution along the span are given in which a better account is taken of the distribution of circulation over te area than in the Prandtl lifting-line theory. The methods are also applicable to wing sweepback. Calculated results for the two methods were in agreement.
Lift Increase by Blowing Out Air, Tests on Airfoil of 12 Percent Thickness, Using Various Types of Flap
The NACA 23012-4 airfoil was investigated for the purpose of increasing lift by means of blowing out air from the wing, in conjunction with the effect of plain flap of variable contour and slotted flap of 25 percent chord length. The wing also was provided with a hinged nose, to be deflected at will. Air was blown out frcm the wing immediately in front of the flap; also at the opening between wing and hinged nose,tangentially to the surface of the wing. Another device employed to increase maximum lift was a movable slat, to be opened to form a clot. Lift was measured in relation to the volume of blown-out air and considerable increases were observed with increasing volume.
The Load Distribution in Bolted or Riveted Joints in Light-Alloy Structures
This report contains a theoretical discussion of the load distribution in bolted or riveted joints in light-alloy structures which is applicable not only for loads below the limit of proportionality but also for loads above this limit. The theory is developed for double and single shear joints. The methods given are illustrated by numerical examples and the values assumed for the bolt (or rivet) stiffnesses are based partly on theory and partly on known experimental values. It is shown that the load distribution does not vary greatly with the bolt (or rivet) stiffnesses and that for design purposes it is usually sufficient to know their order of magnitude. The theory may also be directly used for spot-welded structures and, with small modifications, for seam-welded structures, The computational work involved in the methods described is simple and may be completed in a reasonable time for most practical problems. A summary of earlier theoretical and experimental investigations on the subject is included in the report.
Method of characteristics for three-dimensional axially symmetrical supersonic flows
An approximation method for three-dimensional axially symmetrical supersonic flows is developed; it is based on the characteristics theory (represented partly graphically, partly analytically). Thereafter this method is applied to the construction of rotationally symmetrical nozzles. (author).
The Monoplane as a Lifting Vortex Surface
In Prandtl's airfoil theory the monoplane was replaced by a single lifting vortex line and yielded fairly practical results. However, the theory remained restricted to the straight wing. Yawed wings and those curved in flight direction could not be computed with this first approximation; for these the chordwise lift distribution must be taken into consideration. For the two-dimensional problem the transition from the lifting line to the lifting surface has been explained by Birnbaum. In the present report the transition to the three-dimensional problem is undertaken. The first fundamental problem involves the prediction of flow, profile, and drag for prescribed circulation distribution on the straight rectangular wing, the yawed wing for lateral boundaries parallel to the direction of flight, the swept-back wing, and the rectangular wing in slipping, with the necessary series developments for carrying through the calculations, the practical range of convergence of which does not comprise the wing tips or the break point of the swept-back wing. The second problem concerns the calculation of the circulation distribution with given profile for a slipping rectangular monoplane with flat profile and aspect ratio 6, and a rectangular wing with cambered profile and variable aspect ratio-the latter serving as check of the so-called conversion formulas of the airfoil theory.
On Combustion in a Turbulent Flow
The characteristics introduced by the turbulence in the process of the flame propagation are considered. On the basis of geometrical and dimensional considerations an expression is obtained for the velocity of the flame propagation in a flow of large scale of turbulence.
On the Application of the Energy Method to Stability Problems
Since stability problems have come into the field of vision of engineers, energy methods have proved to be one of the most powerful aids in mastering them. For finding the especially interesting critical loads special procedures have evolved that depart somewhat from those customary in the usual elasticity theory. A clarification of the connections seemed desirable,especially with regard to the post-critical region, for the treatment of which these special methods are not suited as they are. The present investigation discusses this question-complex (made important by shell construction in aircraft) especially in the classical example of the Euler strut, because in this case - since the basic features are not hidden by difficulties of a mathematical nature - the problem is especially clear. The present treatment differs from that appearing in the Z.f.a.M.M. (1938) under the title "Uber die Behandlung von Stabilittatsproblemen mit Hilfe der energetischen Methode" in that, in order to work out the basic ideas still more clearly,it dispenses with the investigation of behavior at large deflections and of the elastic foundation;in its place the present version gives an elaboration of the 6th section and (in its 7 th and 8th secs.)a new example that shows the applicability of the general criterion to a stability problem that differs from that of Euler in many respects.
On the Problems of Chaplygin for Mixed Sub-and Supersonic Flows
There are investigated the problems of the flow of a supersonic jet out of a vessel with plane side walls and the problem of the supersonic flow about a wedge when there is a zone of local subsonic velocities ahead of the wedge.
On the Theory of the Unsteady Motion of an Airfoil
The paper presents a systematical analysis of the problem of the determination of the unsteady motion about an airfoil moving in an infinite fluid that contains a system of vortices and the determination of the hydrodynamical forces acting on the airfoil. The hydrodynamical problem is reduced to the determination of the function f (xi) which transforms conformally the external region of the airfoil into the interior of a circle. The proposed methods of determining the irrotational motion of a fluid that is produced by any motion of the airfoil are especially simple and effective if the function f (xi) is rational. As an example the flow is determined for the case of an arbitrary motion of an airfoil of the Joukowsky type. The formulas obtained for the determination of the hydrodynamical forces by means of contour integration are similar to those given by S. Chaplygin. These formulas are used to determine the force acting on the airfoil in the cases where the unsteady motion is potential throughout and the circulation about the airfoil is constant and also when the fluid contains a system of vortices. A full discussion is given of the concept of virtual masses together with practical formulas for computing the virtual mass coefficients.
On the Vortex Sound from Rotating Rods
The motion of different bodies imersed in liquid or gaseous media is accompanied by characteristic sound which is excited by the formation of unstable surfaces of separation behind the body, usually disintegrating into a system of discrete vortices(such as the Karman vortex street due to the flow about an infintely long rod, etc.).In the noise from fans,pumps,and similar machtnery, vortexnQif3eI?Yequently predominates. The purpose of this work is to elucidate certain questions of the dependence ofthis sound upon the aerodynamic parameters and the tip speed of the rotating rods,or blades. Although scme material is given below,insufficientto calculate the first rough approximation to the solution of this question,such as the mechanics of vortex formation,never the less certain conclusions maybe found of practical application for the reduction of noise from rotating blades.
The Oscillating Circular Airfoil on the Basis of Potential Theory
Proceeding from the thesis by W. Kinner the present report treats the problem of the circular airfoil in uniform airflow executing small oscillations, the amplitudes of which correspond to whole functions of the second degree in x and y. The pressure distribution is secured by means of Prandtl's acceleration potential. It results in a system of linear equations the coefficients of which can be calculated exactly with the aid of exponential functions and Hankel's functions. The equations necessary are derived in part I; the numerical calculation follows in part II.
Possibilities of Reducing the Length of Axial Superchargers for Aircraft Motors
Axial blowers are gaining importance as aircraft engine superchargers. However, the pressure head obtainable per stage is small. Due to the necessary great number of stages, the physical length of the blower becomes too great for an airworthy device. This report discusses several types of construction that permit a reduction in the length of the blower.
Practical Possibilities of High-Altitude Flight with Exhaust-Gas Turbines in Connection with Spark Ignition Engines Comparative Thermodynamic and Flight Mechanical Investigations
As a means of preparing for high-altitude flight with spark-ignition engines in conjunction with exhaust-gas turbosuperchargers, various methods of modifying the exhaust-gas temperatures, which are initially higher than a turbine can withstand are mathematically compared. The thermodynamic results first obtained are then examined with respect to the effect on flight speed, climbing speed, ceiling, economy, and cruising range. The results are so presented in a generalized form that they may be applied to every appropriate type of aircraft design and a comparison with the supercharged engine without exhaust-gas turbine can be made.