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The Inertia Coefficients of an Airship in a Frictionless Fluid

Description: The apparent inertia of an airship hull is examined. The exact solution of the aerodynamical problem is studied for hulls of various shapes with special attention given to the case of an ellipsoidal hull. So that the results for the ellipsoidal hull may be readily adapted to other cases, they are expressed in terms of the area and perimeter of the largest cross section perpendicular to the direction of motion by means of a formula involving a coefficient kappa which varies only slowly when the shape of the hull is changed, being 0.637 for a circular or elliptic disk, 0.5 for a sphere, and about 0.25 for a spheroid of fineness ratio. The case of rotation of an airship hull is investigated and a coefficient is defined with the same advantages as the corresponding coefficient for rectilinear motion.
Date: December 1, 1979
Creator: Bateman, H.

Flow and Drag Formulas for Simple Quadrics

Description: The pressure distribution and resistance found by theory and experiment for simple quadrics fixed in an infinite uniform stream of practically incompressible fluid are calculated. The experimental values pertain to air and some liquids, especially water; the theoretical refer sometimes to perfect, again to viscid fluids. Formulas for the velocity at all points of the flow field are given. Pressure and pressure drag are discussed for a sphere, a round cylinder, the elliptic cylinder, the prolate and oblate spheroid, and the circular disk. The velocity and pressure in an oblique flow are examined.
Date: December 1, 1979
Creator: Zahm, A. F.

Flow and Force Equations for a Body Revolving in a Fluid

Description: A general method for finding the steady flow velocity relative to a body in plane curvilinear motion, whence the pressure is found by Bernoulli's energy principle is described. Integration of the pressure supplies basic formulas for the zonal forces and moments on the revolving body. The application of the steady flow method for calculating the velocity and pressure at all points of the flow inside and outside an ellipsoid and some of its limiting forms is presented and graphs those quantities for the latter forms. In some useful cases experimental pressures are plotted for comparison with theoretical. The pressure, and thence the zonal force and moment, on hulls in plane curvilinear flight are calculated. General equations for the resultant fluid forces and moments on trisymmetrical bodies moving through a perfect fluid are derived. Formulas for potential coefficients and inertia coefficients for an ellipsoid and its limiting forms are presented.
Date: December 1, 1979
Creator: Zahm, A. F.

General Potential Theory of Arbitrary Wing Sections

Description: The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.
Date: December 1, 1979
Creator: Theodorsen, T. & Garrick, I. E.

General Theory of Aerodynamic Instability and the Mechanism of Flutter

Description: The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.
Date: December 1, 1979
Creator: Theodorsen, Theodore

Blockage Corrections for Three-Dimensional-Flow Closed-Throat Wind Tunnels, with Consideration of the Effect of Compressibility

Description: Theoretical blockage corrections are presented for a body of revolution and for a three-dimensional, unswept wing in a circular or rectangular wind tunnel. The theory takes account of the effects of the wake and of the compressibility of the fluid, and is based on the assumption that the dimensions of the model are small in comparison with those of the tunnel throat. Formulas are given for correcting a number of the quantities, such as dynamic pressure and Mach number, measured in wind tunnel tests. The report presents a summary and unification of the existing literature on the subject.
Date: January 1, 1951
Creator: Herriot, J. G.

Applications of Modern Hydrodynamics to Aeronautics. Part 1: Fundamental Concepts and the Most Important Theorems. Part 2: Applications

Description: A discussion of the principles of hydrodynamics of nonviscous fluids in the case of motion of solid bodies in a fluid is presented. Formulae are derived to demonstrate the transition from the fluid surface to a corresponding 'control surface'. The external forces are compounded of the fluid pressures on the control surface and the forces which are exercised on the fluid by any solid bodies which may be inside of the control surfaces. Illustrations of these formulae as applied to the acquisition of transformations from a known simple flow to new types of flow for other boundaries are given. Theoretical and experimental investigations of models of airship bodies are presented.
Date: 1979?~
Creator: Prandtl, L.

The Minimum Induced Drag of Aerofoils

Description: Equations are derived to demonstrate which distribution of lifting elements result in a minimum amount of aerodynamic drag. The lifting elements were arranged (1) in one line, (2) parallel lying in a transverse plane, and (3) in any direction in a transverse plane. It was shown that the distribution of lift which causes the least drag is reduced to the solution of the problem for systems of airfoils which are situated in a plane perpendicular to the direction of flight.
Date: December 1, 1979
Creator: Munk, M. M.

The Aerodynamic Forces on Airship Hulls

Description: The new method for making computations in connection with the study of rigid airships, which was used in the investigation of Navy's ZR-1 by the special subcommittee of the National Advisory Committee for Aeronautics appointed for this purpose is presented. The general theory of the air forces on airship hulls of the type mentioned is described and an attempt was made to develop the results from the very fundamentals of mechanics.
Date: 1979?~
Creator: Munk, M. M.

Effects of sweepback on boundary layer and separation

Description: Following a law of stress adopted in the Navier-Stokes equations, the configuration of the viscous flow in planes at right angles to the axis of an infinite cylinder is found to be independent of the axial motion of the cylinder. In the limiting case of a yawed or swept wing of very high aspect ratio, certain boundary-layer and separation phenomena are thus determined independently by the crosswise component of velocity. It follows that the effect of sweepback is to increase the area of stable laminar flow and to decrease the lift coefficient at which flow separation occurs.
Date: January 1, 1947
Creator: Jones, Robert T

Flight investigation on a fighter-type airplane of factors which affect the loads and load distributions on the vertical tail surfaces during rudder kicks and fishtails

Description: Results are presented of a flight investigation conducted on a fighter-type airplane to determine the factors which affect the loads and load distributions on the vertical tail surfaces in maneuvers. An analysis is made of the data obtained in steady flight, rudder kicks, and fishtail maneuvers. For the rudder kicks, the significant loads were the "deflection load" resulting from an abrupt control deflection and the "dynamic load" consisting of a load corresponding to the new static equilibrium condition for the rudder deflected plus a load due to a transient overshoot. The minimum time to reach the maximum control deflection attainable by the pilot in any flight condition was found to be a constant. In the fishtail maneuvers, it was found that the pilot tends to deflect the rudder in phase with the natural frequency of the airplane. The maximum loads measured in fishtails were of the same order of magnitude as those from a rudder kick in which the rudder is returned to zero at the time of maximum sideslip.
Date: January 1, 1947
Creator: Boshar, John

Spark-timing control based on correlation of maximum-economy spark timing, flame-front travel, and cylinder-pressure rise

Description: An investigation was conducted on a full-scale air-cooled cylinder in order to establish an effective means of maintaining maximum-economy spark timing with varying engine operating conditions. Variable fuel-air-ratio runs were conducted in which relations were determined between the spark travel, and cylinder-pressure rise. An instrument for controlling spark timing was developed that automatically maintained maximum-economy spark timing with varying engine operating conditions. The instrument also indicated the occurrence of preignition.
Date: January 1, 1947
Creator: Cook, Harvey A.; Heinicke, Orville H. & Haynie, William H.

Critical stress of thin-walled cylinders in axial compression

Description: Empirical design curves are presented for the critical stress of thin-wall cylinders loaded in axial compression. These curves are plotted in terms of the nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75.
Date: January 1, 1947
Creator: Batdorf, S B; Schildcrout, Murry & Stein, Manuel

A theory of unstaggered airfoil cascades in compressible flow

Description: 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.
Date: January 1, 1947
Creator: Spurr, Robert A & Allen, H Julian

Investigations of effects of surface temperature and single roughness elements on boundary-layer transition

Description: The laminar boundary layer and the position of the transition point were investigated on a heated flat plate. It was found that the Reynolds number of transition decreased as the temperature of the plate is increased. It is shown from simple qualitative analytical considerations that the effect of variable viscosity in the boundary layer due to the temperature difference produces a velocity profile with an inflection point if the wall temperature is higher than the free-stream temperature. This profile is confirmed by measurements. The instability of inflection-point profiles is discussed. Studies of the flow in the wake of large, two-dimensional roughness elements are presented. It is shown that a boundary-layer can separate and reattach itself to the wall without having transition take place.
Date: January 1, 1947
Creator: Liepmann, Hans W & Fila, Gertrude H

A thermodynamic study of the turbojet engine

Description: Charts are presented for computing thrust, fuel consumption, and other performance values of a turbojet engine for any given set of operating conditions and component efficiencies. The effects of pressure losses in the inlet duct and the combustion chamber, of variation in physical properties of the gas as it passes through the system, of reheating of the gas due to turbine losses, and of change in mass flow by the addition of fuel are included. The principle performance chart shows the effects of primary variables and correction charts provide the effects of secondary variables and of turbine-loss reheat on the performance of the system. The influence of characteristics of a given compressor and turbine on performance of a turbojet engine containing a matched set of these given components is discussed for cases of an engine with a centrifugal-flow compressor and of an engine with an axial-flow compressor.
Date: January 1, 1947
Creator: Pinkel, Benjamin & Karp, Irvin M

Damping in pitch and roll of triangular wings at supersonic speeds

Description: A method is derived for calculating the damping coefficients in pitch and roll for a series of triangular wings and a restricted series of sweptback wings at supersonic speeds. The elementary "supersonic source" solution of the linearized equation of motion is used to find the potential function of a line of doublets, and the flows are obtained by surface distributions of these doublet lines. The damping derivatives for triangular wings are found to be a function of the ratio of the tangent of the apex angle to the tangent of the Mach angle. As this ratio becomes equal to and greater than 1.0 for triangular wings, the damping derivatives, in pitch and in roll, become constant. The damping derivative in roll becomes equal to one-half the value calculated for an infinite rectangular wing, and the damping derivative in pitch for pitching about the apex becomes equal to 3.375 times that of an infinite rectangular wing.
Date: January 1, 1948
Creator: Brown, Clinton E & Adams, Mac C