"In the walls of heat exchangers composed of noncircular passages, the temperature varies in the circumferential direction because of local variations of the heat-transfer coefficients. A prediction of the magnitude of this variation is necessary in order to determine the region of highest temperature and in order to determine the admissible operating temperatures. A method for the determination of these temperature distributions and of the heat-transfer characteristics of a special type of heat exchanger is developed" (p. 383).

"An analytic method for the design of automatic controls is developed that starts from certain arbitrary criterions on the behavior of the controlled system and gives those physically realizable equations that the control system can follow in order to realize this behavior. The criterions used are developed in the form of certain time integrals. General results are shown for systems of second order and of any number of degrees of freedom. Detailed examples for several cases in the control of a turbojet engine are presented" (p. 207).

"The problem of transient lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchoff's formula is applied so that the analysis is reduced, just as in the steady state, to an investigation of sources and doublets. The applications include the evaluation of indicial lift and pitching-moment curves for two-dimensional sinking and pitching wings flying at Mach numbers equal to 0, 0.8, 1.0, 1.2 and 2.0" (p. 393).

The significant findings of a theoretical study of column behavior in the plastic stress range are presented. When the behavior of a straight column is regarded as the limiting behavior of an imperfect column as the initial imperfection (lack of straightness) approaches zero, the departure from the straight configuration occurs at the tangent-modulus load. Without such a concept of the behavior of a straight column, one is led to the unrealistic conclusion that lateral deflection of the column can begin at any load between the tangent-modulus value and the Euler load, based on the original elastic modulus. A family of curves showing load against lateral deflection is presented for idealized h-section columns of various lengths and of various materials that have a systematic variation of their stress-strain curves.

"The formulas of subsonic and supersonic wing theory for source, doublet, and vortex distributions are reviewed and a systematic presentation is provided which relates these distributions to the pressure and to the vertical induced velocity in the plane of the wing. It is shown that care must be used in treating the singularities involved in the analysis and that the order of integration is not always reversible. Concepts suggested by the irreversibility of order of integration are shown to be useful in the inversion of singular integral equations when operational techniques are used. A number of examples are given to illustrate the methods presented, attention being directed to supersonic flight speed" (p. 1267).

From Summary: "This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. Nondimensional charts to simplify some temperature-distribution calculations are also given."

A vector study of the partial-differential equation of steady linearized supersonic flow is presented. General expressions which relate the velocity potential in the stream to the conditions on the disturbing surfaces, are derived. In connection with these general expressions the concept of the finite part of an integral is discussed. A discussion of problems dealing with planar bodies is given and the conditions for the solution to be unique are investigated. Problems concerning nonplanar systems are investigated, and methods are derived for the solution of some simple nonplanar bodies. The surface pressure distribution and the damping in roll are found for rolling tails consisting of four, six, and eight rectangular fins for the Mach number range where the region of interference between adjacent fins does not affect the fin tips.

From Summary: "Measurements of base pressure are presented for 29 blunt-trailing-edge wings having an aspect ratio of 3.0 and various airfoil profiles. The different profiles comprised thickness ratios between 0.05 and 0.10, boattail angles between -2.9 degrees and 20 degrees, and ratios of trailing-edge thickness to airfoil thickness between 0.2 and 1.0. The tests were conducted at Mach numbers of 1.25, 1.5, 2.0, and 3.1. For each Mach number, the Reynolds number and angle of attack were varied. The lowest Reynolds number investigated was 0.2 x 10(6) and the highest was 3.5 x 10(6). Measurements on each wing were obtained separately with turbulent flow and laminar flow in the boundary layer. Span-wise surveys of the base pressure were conducted on several wings."

"Porcelain-enamel ground coats were prepared and applied under conditions that gave various degrees of adherence between enamel and a low-carbon steel (enameling iron). The variations in adherence were produced by (a) varying the amount of cobalt-oxide addition in the frit, (b) varying the type of metallic-oxide addition in the frit, keeping the amount constant at 0.8 weight percent, (c) varying the surface treatment of the metal before application of the enamel, by pickling, sandblasting, and polishing, and (d) varying the time of firing of the enamel containing 0.8 percent of cobalt oxide. Specimens of each enamel were given the standard adherence test of the Porcelain Enamel Institute" (p. 239).

Equations are presented for the attenuation characteristics of single-chamber and multiple-chamber mufflers of both the expansion-chamber and resonator types, for tuned side-branch tubes, and for the combination of an expansion chamber with a resonator. Experimental curves of attenuation plotted against frequency are presented for 77 different mufflers with a reflection-free tailpipe termination. The experiments were made at room temperature without flow; the sound source was a loud-speaker. A method is given for including the tailpipe reflections in the calculations. Experimental attenuation curves are presented for four different muffler-tailpipe combinations, and the results are compared with the theory. The application of the theory to the design of engine-exhaust mufflers is discussed, and charts are included for the assistance of the designer.

"The basic equations of Timoshenko for the motion of vibrating nonuniform beams, which allow for effects of transverse shear deformation and rotary inertia, are presented in several forms, including one in which the equations are written in the directions of the characteristics. The propagation of discontinuities in moment and shear, as governed by these equations, is discussed. Numerical traveling-wave solutions are obtained for some elementary problems of finite uniform beams for which the propagation velocities of bending and shear discontinuities are taken to be equal" (p. 359).

"Measurements, principally with a hot-wire anemometer, were made in fully developed turbulent flow in a 10-inch pipe at speeds of approximately 10 and 100 feet per second. Emphasis was placed on turbulence and conditions near the wall. The results include relevant mean and statistical quantities, such as Reynolds stresses, triple correlations, turbulent dissipation, and energy spectra" (p. 1).

"The motions, hydrodynamic loads, and pitching moments experienced by V-bottom seaplanes during step-landing impacts are analyzed and the theoretical results are compared with experimental data. In the analysis, the primary flow about the immersed portion of a keeled hull or float is considered to occur in transverse flow planes and the concept of virtual mass is applied to determined the reaction of the water to the motions of the seaplane. The entire immersion process is analyzed from the instant of initial contact until the seaplane rebounds from the water surfaces" (p. 953).

A theoretical analysis of helicopter maneuver stability is made and the results are compared with experimental results for both a single and a tandem rotor helicopter. Techniques are described for measuring in flight the significant stability derivatives for use with the theory to aid in design studies of means for achieving marginal maneuver stability for a prototype helicopter.

From Summary: "The sound-pressure field of a rotating propeller in forward flight in free space is analyzed by replacing the normal-pressure distribution over the propeller associated with thrust and torque by a distribution of acoustic pressure doublets acting at the propeller disk and subject to uniform rectilinear motion. The basic element used to synthesize the field is the pressure field of a concentrated force moving uniformly at subsonic speeds, for which an expression generalizing one of Lamb's for the fixed concentrated force is given. The sound field is expressed by integration over the propeller disk, and also by integration over an effective ring, and is given both for the near pressure field and, in a simpler form, for the far field. Some illustrated examples are calculated and discussed."

"Theoretically derived charts and equations are presented by which tail-rotor design studies of directional trim and control response at low forward speed can be conveniently made. The charts can also be used to obtain the main-rotor stability derivatives of thrust with respect to collective pitch and angle of attack at low forward speeds. The use of the charts and equations for tail-rotor design studies is illustrated. Comparisons between theoretical and experimental results are presented. The charts indicate, and flight tests confirm, that the region of vortex roughness which is familiar for the main rotor is also encountered by the tail rotor and that prolonged operation at the corresponding flight conditions would be difficult" (p. 1).

"Stewartson's transformation is applied to the laminar compressible boundary-layer equations and the requirement of similarity is introduced, resulting in a set of ordinary nonlinear differential equations previously quoted by Stewartson, but unsolved. The requirements of the system are Prandtl number of 1.0, linear viscosity-temperature relation across the boundary layer, an isothermal surface, and the particular distributions of free-stream velocity consistent with similar solutions. This system admits axial pressure gradients of arbitrary magnitude, heat flux normal to the surface, and arbitrary Mach numbers" (p. 1).

From Summary: "A method of computing span loads and the resulting rolling moments for sideslipping wings of arbitrary plan form in incompressible flow is derived. The method requires that the span load at zero sideslip be known for the wing under consideration. Because this information is available for a variety of wings, this requirement should not seriously restrict the application of the present method. The basic method derived herein requires a mechanical differentiation and integration to obtain the rolling moment for the general wing in sideslip."

"The lifting-surface sidewash behind rolling triangular wings has been derived for a range of supersonic Mach numbers for which the wing leading edges remain swept behind the mark cone emanating from the wing apex. Variations of the sidewash with longitudinal distance in the vertical plane of symmetry are presented in graphical form. An approximate expression for the sidewash has been developed by means of an approach using a horseshoe-vortex approximate-lifting-line theory" (p. 455).

A theoretical study is made of the pressures, loadings, forces, and vortex wake associated with certain cruciform wing arrangements. For 45 degree bank, the wake of a cruciform wing is treated numerically with 40 vortices and analytically with 4 vortices. Comparisons are made with water-tank measurements, and the calculation of loads on cruciform tails by reverse flow considered.

"The similarity rules for linearized compressible flow theory (Gothert's rule and its supersonic counterpart) are extended to second order. It is shown that any second-order subsonic flow can be related to "nearly incompressible" flow past the same body, which can be calculated by the Janzen-Rayleigh method" (p. 925).

Results are presented of an experimental and theoretical investigation of the growth of transverse velocity disturbances in the shear region caused by a flame in a duct. In the theoretical stability analysis, a flow field arising from a flame in a duct was analyzed. The flow was neutrally stable to symmetric disturbances and unstable to antisymmetric ones. In the experimental part of the program disturbances of various frequencies were imposed on a flame stabilized in a duct, and the effects were measured by shadow photography and photomultiplier-probe surveys.

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Report presents the results of an investigation of the effects of fuel properties and of a number of fuel additives on combustion-chamber carbon deposition and exhaust-gas smoke formation in a single tubular turbojet-engine combustor. Limited tests were conducted with a number of the fuels in several full-scale turbojet engines to verify single-combustor data.