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

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

### The Theory of the Pitot and Venturi Tubes, Part 2

**Date:**January 1, 1989

**Creator:**Buckingham, E.

**Description:**None

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### The Aerodynamic Forces on Airship Hulls

**Date:**December 1, 1979

**Creator:**Munk, M. M.

**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.

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

**Date:**December 1, 1979

**Creator:**Prandtl, L.

**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.

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### Elements of the Wing Section Theory and of the Wing Theory

**Date:**December 1, 1979

**Creator:**Munk, Max M.

**Description:**Results are presented of the theory of wings and of wing sections which are of immediate practical value. They are proven and demonstrated by the use of the simple conceptions of kinetic energy and momentum only.

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### Flow and Drag Formulas for Simple Quadrics

**Date:**December 1, 1979

**Creator:**Zahm, A. F.

**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.

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### Flow and Force Equations for a Body Revolving in a Fluid

**Date:**December 1, 1979

**Creator:**Zahm, A. F.

**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.

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### General Potential Theory of Arbitrary Wing Sections

**Date:**December 1, 1979

**Creator:**Theodorsen, T. & Garrick, I. E.

**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.

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### General Theory of Aerodynamic Instability and the Mechanism of Flutter

**Date:**December 1, 1979

**Creator:**Theodorsen, Theodore

**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.

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### The Inertia Coefficients of an Airship in a Frictionless Fluid

**Date:**December 1, 1979

**Creator:**Bateman, H.

**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.

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### The Minimum Induced Drag of Aerofoils

**Date:**December 1, 1979

**Creator:**Munk, M. M.

**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.

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### One-dimensional flows of an imperfect diatomic gas

**Date:**January 1, 1959

**Creator:**unknown

**Description:**With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author).

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### An analysis of pressure studies and experimental and theoretical downwash and sidewash behind five pointed-tip wings at supersonic speeds

**Date:**January 1, 1958

**Creator:**Boatright, William B

**Description:**Flow-angle and pressure surveys behind five, thin, pointed-tip wings of varying plan form have been made at Mach numbers 1.62 and 2.41. Schlieren studies at a Mach number 1.93 for the same five plan-form wings were made to illustrate the behavior of the vortex sheet. The surveys were conducted at 1.5, 3, and 4 root chords behind three triangular wings of 50 degree, 63 degree, and 72 degree leading-edge sweep angle, and behind the 50 degree triangular wing reversed. The flow behind a pointed-tip wing having a sweptback leading edge and a sweptforward trailing edge (both 50 degrees) was also surveyed. Experiment and one of the theoretical methods are compared for the reversed triangular wing and the pointed-tip wing with the 50 degree sweptback leading edge and sweptforward trailing edge.

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### Approximate analysis of effects of large deflections and initial twist on torsional stiffness of a cantilever plate subjected to thermal stresses

**Date:**January 1, 1958

**Creator:**Heldenfels, Richard R & Vosteen, Louis F

**Description:**An approximate analysis of the nonlinear effects of initial twist and large deflections on the torsional stiffness of a cantilever plate subjected to a nonuniform temperature distribution is presented. The Von Karman large-deflection equations are satisfied through the use of a variational principle. The results show that initial twist and applied moments can have significant effects on the changes in stiffness produced by nonuniform heating, particularly in the region of the buckling temperature difference. Results calculated by this approximate analysis are in satisfactory agreement with measured torsional deformations and changes in natural frequency. (author).

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### Area-suction boundary-layer control as applied to the trailing-edge flaps of a 35 degree swept-wing airplane

**Date:**January 1, 1958

**Creator:**Cook, Woodrow L; Anderson, Seth B & Cooper, George E

**Description:**A wind-tunnel investigation was made to determine the effects on the aerodynamic characteristics of a 35 degree swept-wing airplane of applying area-suction boundary-layer control to the trailing-edge flaps. Flight tests of a similar airplane were then conducted to determine the effect of boundary-layer control in the handling qualities and operation of the airplane, particularly during landing. The wind-tunnel and flight tests indicated that area suction applied to the trailing-edge flaps produced significant increases in flap lift increment. Although the flap boundary-layer control reduced the stall speed only slightly, a reduction in minimum comfortable approach speed of about 12 knots was obtained.

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### Blowing-type boundary-layer control as applied to the trailing-edge flaps of a 35 degree swept-wing airplane

**Date:**January 1, 1958

**Creator:**Kelly, Mark W; Anderson, Seth B & Innis, Robert C

**Description:**A wind-tunnel investigation was made to determine the effects on the aerodynamic characteristics of a 35 degree swept-wing airplane of applying blowing-type boundary-layer control to the trailing-edge flaps. Flight tests of a similar airplane were then conducted to determine the effects of boundary-layer control on the handling qualities and operation of the airplane, particularly during landing and take-off. The wind-tunnel and flight tests indicated that blowing over the flaps produced large increases in flap lift increment, and significant increases in maximum lift. The use of blowing permitted reductions in the landing approach speeds of as much as 12 knots.

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### Boron and zirconium from crucible refractories in a complex heat-resistant alloy

**Date:**January 1, 1958

**Creator:**Decker, R F; Rowe, John P & Freeman, J W

**Description:**In a laboratory study of the factors involved in the influence of induction vacuum melting on 55ni-20cr-15co-4mo-3ti-3al heat resistant alloy, it was found that the major factor was the type of ceramic used as the crucible. The study concluded that trace amounts of boron or zirconium derived from reaction of the melt with the crucible refactories improved creep-rupture properties at 1,600 degrees F. Boron was most effective and, in addition, markedly improved hot-workability.

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### Calculated and measured stresses in simple panels subject to intense random acoustic loading including the near noise field of a turbojet engine

**Date:**January 1, 1958

**Creator:**Lassiter, Leslie W & Hess, Robert W

**Description:**Flat 2024-t3 aluminum panels measuring 11 inches by 13 inches were tested in the near noise fields of a 4-inch air jet and turbojet engine. The stresses which were developed in the panels are compared with those calculated by generalized harmonic analysis. The calculated and measured stresses were found to be in good agreement. In order to make the stress calculations, supplementary data relating to the transfer characteristics, damping, and static response of flat and curved panels under periodic loading are necessary and were determined experimentally. In addition, an appendix containing detailed data on the near pressure field of the turbojet engine is included.

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### Characteristics of the Langley 8-foot transonic tunnel with slotted test section

**Date:**January 1, 1958

**Creator:**Wright, Ray H; Ritchie, Virgil S & Pearson, Albin O

**Description:**A large wind tunnel, approximately 8 feet in diameter, has been converted to transonic operation by means of slots in the boundary extending in the direction of flow. The usefulness of such a slotted wind tunnel, already known with respect to the reduction of the subsonic blockage interference and the production of continuously variable supersonic flows, has been augmented by devising a slot shape with which a supersonic test region with excellent flow quality could be produced. Experimental locations of detached shock waves ahead of axially symmetric bodies at low supersonic speeds in the slotted test section agreed satisfactorily with predictions obtained by use of existing approximate methods.

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### A comparative analysis of the performance of long-range hypervelocity vehicles

**Date:**January 1, 1958

**Creator:**Eggers, Alfred J , Jr; Allen, H Julian & Neice, Stanford E

**Description:**Long-range hypervelocity vehicles are studied in terms of their motion in powered flight. Powered flight is analyzed for an idealized propulsion system which approximates rocket motors. Unpowered flight is characterized by a return to earth along a ballistic, skip, or glide trajectory. Only those trajectories are treated which yield the maximum range for a given velocity at the end of powered flight. Aerodynamic heating is treated in a manner similar to that employed previously by the senior authors in studying ballistic missiles (NACA rep. 1381), with the exception that radiant as well as convective heat transfer is considered in connection with glide and skip vehicles. As a final performance consideration, it is shown that on the basis of equal ratios of mass at take-off to mass at the end of powered flight, the hypervelocity vehicle compares favorably with the supersonic airplane for ranges in the neighborhood of and greater than one half the circumference of the earth. In the light of this and previous findings, it is concluded that the ballistic and glide vehicles have, in addition to the advantages usually ascribed to great speed, the attractive possibility of providing relatively efficient long-range flight.

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### Compressible laminar boundary layer over a yawed infinite cylinder with heat transfer and arbitrary Prandtl number

**Date:**January 1, 1958

**Creator:**Reshotko, Eli & Beckwith, Ivan E

**Description:**The equations are presented for the development of the compressible laminar boundary layer over a yawed infinite cylinder. For compressible flow with a pressure gradient the chordwise and spanwise flows are not independent. Using the Stewartson transformation and a linear viscosity-temperature relation yields a set of three simultaneous ordinary differential equations in a form yielding similar solutions. These equations are solved for stagnation-line flow for surface temperatures from zero to twice the free-stream stagnation temperature and for a wide range of yaw angle and free-stream Mach number. The results indicate that the effect of yaw on the heat-transfer coefficient at the stagnation line depends markedly on the free-stream Mach number. An unusual result of the solutions is that for large yaw angles and stream Mach numbers the chordwise velocity within the boundary layer exceeds the local external chordwise velocity, even for a highly cooled wall.

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### A correlation of results of flight investigation with results of an analytical study of effects of wing flexibility on wing strains due to gusts

**Date:**January 1, 1958

**Creator:**Shufflebarger, C C; Payne, Chester B & Cahen, George L

**Description:**An analytical study of the effects of wing flexibility on wing strains due to gusts has been made for four spanwise stations of a four-engine bomber airplane, and the results have been correlated with results of a previous flight investigation.

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### Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades

**Date:**January 1, 1958

**Creator:**Houbolt, John C & Brooks, George W

**Description:**The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper. Special attention is given the terms which are not included in previous theories. These terms are largely coupling-type terms associated with the centrifugal forces. Methods of solution of the equations of motion are indicated by selected examples.

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### Ditching investigations of dynamic models and effects of design parameters on ditching characteristics

**Date:**January 1, 1958

**Creator:**Fisher, Lloyd J & Hoffman, Edward L

**Description:**Data from ditching investigations conducted at the Langley Aeronautical Laboratory with dynamic scale models of various airplanes are presented in the form of tables. The effects of design parameters on the ditching characteristics of airplanes, based on scale-model investigations and on reports of full-scale ditchings, are discussed. Various ditching aids are also discussed as a means of improving ditching behavior.

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### Drag minimization for wings and bodies in supersonic flow

**Date:**January 1, 1958

**Creator:**Heaslet, Max A & Fuller, Franklyn B

**Description:**The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

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