Report discussing theoretical basis of the acoustics of a moving nonhomogeneous medium. Experiments that illustrate or confirm some of the theoretical explanation or derivation of these acoustics are also included.

Report presenting an investigation to determine the carry loads and mutual aerodynamic interference effects from high-speed wind-tunnel tests and the drop characteristics of the X-15 through the B-52 flow field from low-speed dynamic-model drop tests and six-degree-of-freedom calculations. The X-15 installation was found to increase drag at cruise conditions by approximately 15 percent.

"The unsteady aerodynamic forces, [based on two-dimensional incompressible flow considerations], are determined for an unstaggered cascade, the blades of which are vibrating in phase in an approach flow parallel to the blades" (p. 1).

The influence of the deflected flow caused by the fuselage (especially by unsymmetrical attitudes) on the lift and the rolling moment due to sideslip has been discussed for infinitely long fuselages with circular and elliptical cross section. The aim of this work is to add rectangular cross sections and, primarily, to give a principle by which one can get practically usable contours through simple conformal mapping. In a few examples, the velocity field in the wing region and the induced flow produced are calculated and are compared with corresponding results from elliptical and strictly rectangular cross sections.

The technical memorandum briefly summarizes the growth of interest in aeroelastic phenomena as aircraft speed increased and wing designs changed for faster aircraft. Different types of aircraft vibrations are then introduced, and the mathematical basis for the theory behind them is described. Special attention is given to static oscillations, wing flutter, and the flutter of skin panels. The last section of the memorandum deals with the prevention of flutter by design specifications.

From Introduction: "The problem of thrust increase for jet engines by air mixture to the exhaust jet was introduced into aviation techniques by the suggestions of Melot (ref.1). Due to a too general interpretation of several theoretical investigations of A. Busemann (ref.2), so far no practical use has been made of these suggestions. The following considerations show that, in the case of low-pressure mixing according to Melot's suggestions, probably no thrust increase of technical significance will occur for the flight speeds of interest (however, the low-pressure mixture is highly promising for ground test setups and for special power plants of relatively slow sea and land vehicles."

From Summary: "The author first sets forth some observations about the theory of models. Then he established certain general criteria for the construction of dynamically similar models in water and in air, through reference to the perfect fluid equations and to the ones pertaining to viscous flow. It is, in addition, pointed out that there are more cases in which the analogy is possible than is commonly supposed."

From Introduction: "The present report, therefore, deals first, with the distribution of the amplitude of the disturbance over the flow section, that is, the calculation of the characteristic functions and second, with the study of the energy distribution and energy balance of the disturbance motion. The investigations are based upon the disturbances of the laminar flow past a flat plate which are situated exactly at the boundary between amplification and damping (neutral oscillations)."

The problem of shimmy of a castering wheel, such as the nose wheel of a tricycle gear airplane, is treated analytically. The flexibility of the tire is considered to be the primary cause of shimmy. The rather simple theory developed agrees rather well with previous experimental results. The author suggests that shimmy may be eliminated through a suitable choice of landing gear dimensions in lieu of a damper.

The report describes a brief review is made of improvements to an experimental apparatus for time and space correlation designed for study of turbulence. Included is a description of the control of the measurements and a few particular applications.

The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics.

"The shell shall be considered as a three-dimensional continuous medium; for the coordinate surface, the middle surface of the shell shall be assumed parallel to the bounding surfaces. Let alpha and beta be the curvilinear orthogonal coordinates of this surface, coinciding with the lines of principal curvatures, and gamma the distance along the normal from the point (alpha,beta) of the coordinate surface to any point (alpha, beta, gamma) of the shell" (p. 1).

For compressible flow with friction in a cylindrical pipe the momentum, continuity, and heat-transfer equations are examined to determine whether an increase in Mach number ("thermal" Laval nozzle) is obtainable through heat conduction from the gas through the pipe walls. The analysis is based on the assumption that the wall temperature is negligibly small in comparison with the stagnation temperature of the gas. The analysis leads to a negative result. When the gas cooling is increased by also considering radiation to the wall, a limited region at high temperatures is obtained where Mach number increases were theoretically possible. Obtaining this condition practically is considered impossible.

From Introduction: "The fundamental, practically the most important branch of the modern mechanics of a viscous fluid or a gas, is that branch which concerns itself with the study of the boundary layer. The presence of a boundary layer accounts for the origin of the resistance and lift force, the breakdown of the smooth flow about bodies, and other phenomena that are associated with the motion of a body in a real fluid. The concept of boundary layer was clearly formulated by the founder of aerodynamics, N. E. Joukowsky, in his well-known work "On the Form of Ships" published as early as 1890."

"The vortices forming in flowing water behind solid bodies are not represented correctly by the solution of the potential theory nor by Helmholtz's jets. Potential theory is unable to satisfy the condition that the water adheres at the wetted bodies, and its solutions of the fundamental hydrodynamic equations are at variance with the observation that the flow separates from the body at a certain point and sends forth a highly turbulent boundary layer into the free flow. Helmholtz's theory attempts to imitate the latter effect in such a way that it joins two potential flows, jet and still water, nonanalytical along a stream curve" (p. 1).

A comparatively rapid method is presented for determining theoretically the bending stresses of helicopter rotor blades in forward flight. The method is based on the analysis of the properties of a vibrating beam, and its uniqueness lies in the simple solution of the differential equation which governs the motion of the bent blades.

"Graphs and formulas are given with the aid of which all the aerodynamic coefficients required for computing the lateral dynamic stability can be determined. A number of numerical examples are given for obtaining the stability derivatives and solving the characteristic-stability equation. Approximate formulas are derived with the aid of which rapid preliminary computations may be made and the stability coefficients corrected for certain modifications of the airplane" (p. 1).

"The idea is advanced of making a supersonic nozzle by producing one, two, or three successive turns of the whole flow; with the result that the wall contour can be calculated exactly by means of the Prandtl-Meyer "Lost Solution" (p. 1).

"For application in practice for annular radiator fairings and similar arrangements, two new classes of circular cowls are developed by theoretical method, and investigated in a systematic test series regarding their behavior under various working conditions" (p. 1).

"It is shown how one may obtain, in a simple manner, the forms of ring-shaped bodies from existing tables of functions according to the customary method of superposition of flow due to singularities and parallel flow. A number of examples of the forms and pressure distributions of annular source bodies with and without hub body are given, and the inlet conditions of such ring-shaped cowlings are investigated. Furthermore, the annular bodies of finite length are indicated that correspond to Joukowsky profiles for the two-dimensional case" (p. 1).

The investigations carried out in a previous report (NACA TM 1325) concerning the flow about ring-shaped cowlings were extended by taking a circulation about the cowling into consideration. The present second report treats bodies of infinite length with approximately smooth entrance. The circulation was caused by distributing vortex rings of constant density over a stream surface extending to infinity. Furthermore, the influence of a hub body on such cowlings was dealt with.

"The present report presents as a supplement to the fourth report (available as ATI 5045, Air Materiel Command) in the series of investigations concerning the flow about ring-shaped cowlings further wind-tunnel measurements on inlet devices which are to show the influence of the radius of the nose of the cowling on the flow conditions. Moreover, a simple rule for the design of such arrangements, containing a hub in the interior, is suggested" (p. 1).

"The measurements of part V (reference 1) of this series of reports, which concerned comparatively long ring profiles, are supplemented by measurements on shorter rings as they are used for shrouded propellers and cowlings of ring-shaped radiators. Mass-flow coefficients and profile drags are given. Furthermore, it has to be determined how far the potential theory describes the flow phenomenon with sufficient accuracy and whether the present theory for the calculation of thin annular profile yields useful profile forms and is suitable for determination of the mass flow for thick profiles" (p. 1).

The dependence of the maximum incremental velocities and air forces on a circular cowling on the mass flow and the angle of attack of the oblique flow is determined with the aid of pressure-distribution measurements. The particular cowling tested had been partially investigated in NACA TM 1327.