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**Partner:**UNT Libraries Government Documents Department

**Decade:**1970-1979

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

### 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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### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53406/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53413/

### 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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### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53396/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53407/

### An approximate spin design criterion for monoplanes, 1 May 1939

**Date:**January 1, 1976

**Creator:**Seidman, O. & Donlan, C. J.

**Description:**An approximate empirical criterion, based on the projected side area and the mass distribution of the airplane, was formulated. The British results were analyzed and applied to American designs. A simpler design criterion, based solely on the type and the dimensions of the tail, was developed; it is useful in a rapid estimation of whether a new design is likely to comply with the minimum requirements for safety in spinning.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53319/

### Methods of analyzing wind-tunnel data for dynamic flight conditions

**Date:**January 1, 1976

**Creator:**Donlan, C. J. & Recant, I. G.

**Description:**The effects of power on the stability and the control characteristics of an airplane are discussed and methods of analysis are given for evaluating certain dynamic characteristics of the airplane that are not directly discernible from wind tunnel tests alone. Data are presented to show how the characteristics of a model tested in a wind tunnel are affected by power. The response of an airplane to a rolling and a yawing disturbance is discussed, particularly in regard to changes in wing dihedral and fin area. Solutions of the lateral equations of motion are given in a form suitable for direct computations. An approximate formula is developed that permits the rapid estimation of the accelerations produced during pull-up maneuvers involving abrupt elevator deflections.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53322/

### Spin tests of a low-wing monoplane to investigate scale effect in the model test range, May 1941

**Date:**January 1, 1976

**Creator:**Donlan, C. J.

**Description:**Concurrent tests were performed on a 1/16 and a 1/20 scale model (wing spans of 2.64 and 2.11 ft. respectively) of a modern low wing monoplane in the NACA 15 foot free-spinning wind tunnel. Results are presented in the form of charts that afford a direct comparison between the spins of the two models for a number of different conditions. Qualitatively, the same characteristic effects of control disposition, mass distribution, and dimensional modifications were indicated by both models. Quantitatively, the number of turns for recover and the steady spin parameters, with the exception of the inclination of the wing to the horizontal, were usually in good agreement.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53320/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53403/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53404/

### Remarks on the Pressure Distribution over the Surface of an Ellipsoid, Moving Translationally Through a Perfect Fluid

**Date:**December 1, 1979

**Creator:**Munk, Max M.

**Description:**The pressure distribution over ellipsoids when in translatory motion through a perfect fluid is calculated. A method to determine the magnitude of the velocity and of the pressure at each point of the surface of an ellipsoid of rotation is described.

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### Pressure Distribution on Joukowski Wings

**Date:**December 1, 1979

**Creator:**Blumenthal, O.

**Description:**The hydrodynamics and mathematical models as applied to the potential flow about a Joukowski wing are presented.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53400/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53402/

### Graphic Construction of Joukowski Wings

**Date:**December 1, 1979

**Creator:**Trefftz, E.

**Description:**A plot of the cross sectional outline of a Joukowski wing is presented.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc53401/