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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 1979
Creator: Bateman, H.

Propeller charts for the determination of the rotational speed for the maximum ratio of the propulsive efficiency to the specific fuel consumption

Description: A set of propeller operating efficiency charts, based on a coefficient from which the propeller rotational speed has been eliminated, is presented. These charts were prepared with data obtained from tests of full-size metal propellers in the NACA propeller-research tunnel. Working charts for nine propeller-body combinations are presented, including results from tests of dual-rotating propellers. These charts are to be used in the calculation of the range and the endurance of airplanes equipped with constant-speed propellers in which, for given flight conditions, it is desired to determine the propeller revolution speed that gives the maximum ratio of the propulsive efficiency to the specific fuel consumption. The coefficient on which the charts are based may be written in the form of a thrust coefficient or a thrust-power coefficient. A method of using the charts is outlined and sample computations for a typical airplane are included.
Date: December 11, 1940
Creator: Biermann, David & Conway, Robert N.

Some theoretical low-speed span loading characteristics of swept wings in roll and sideslip

Description: The Weissinger method for determining additional span loading for incompressible flow is used to find the damping in roll, the lateral center of pressure of the rolling for wing plan forms of various aspect ratios, taper ratios, and sweep angles. In addition, the applicability of the method to the determination of certain other aerodynamic derivatives is investigated, and corrections for the first-order effects of compressibility are indicated. The agreement obtained between experimentally and theoretically determined values for the aerodynamic coefficients indicates that the method of Weissinger is well suited to the calculation of such resulting aerodynamic derivatives of wings as do not involve considerations of tip suction.
Date: December 22, 1948
Creator: Bird, John D.

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: December 12, 1947
Creator: Brown, Clinton E. & Adams, Mac C.

A method for the calculation of external lift, moment, and pressure drag of slender open-nose bodies of revolution at supersonic speeds

Description: An approximate method is presented for the calculation of the external lift, moment, and pressure drag of slender open-nose bodies of revolution of supersonic speeds. The lift, moment, and pressure drag of a typical ram-jet body shape are calculated at Mach numbers 1.45, 1.60, 1.75, and 3.00; and the lift and moment results are compared with available experimental data. The agreement of the calculated lift and moment data with the experimental data is excellent. The pressure-drag comparison was not presented because of the uncertainty of the amount of skin-friction drag present in the experimental results.
Date: December 29, 1945
Creator: Brown, Clinton E. & Parker, Hermon M.

The torsional strength of wings

Description: This report describes a simple method for calculating the position of the elastic axis of a wing structure having any number of spars. It is shown that strong drag bracing near the top and bottom of a wing greatly increases the torsional strength. An analytical procedure for finding the contribution of the drag bracing to the torsional strength and stiffness is described, based upon the principle of least work, and involving only one unknown quantity. A coefficient for comparing the torsional rigidity of different wings is derived in this report.
Date: December 1928
Creator: Burgess, C. P.

Summary of methods for calculating dynamic lateral stability and response and for estimating aerodynamic stability derivatives

Description: "A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Detailed estimation methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic and supersonic speed conditions" (p. 1).
Date: December 13, 1950
Creator: Campbell, John P. & McKinney, Marion O.

Theoretical and analog studies of the effects of nonlinear stability derivatives on the longitudinal motions of an aircraft in response to step control deflections and to the influence of proportional automatic control

Description: Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.
Date: December 29, 1950
Creator: Curfman, Howard J., Jr.

Theoretical antisymmetric span loading for wings of arbitrary plan form at subsonic speeds

Description: A simplified lifting-surface theory that includes effects of compressibility and spanwise variation of section lift-curve slope is used to provide charts with which antisymmetric loading due to arbitrary antisymmetric angle of attack can be found for wings having symmetric plan forms with a constant spanwise sweep angle of the quarter-chord line. Consideration is given to the flexible wing in roll. Aerodynamic characteristics due to rolling, deflected ailerons, and sideslip of wings with dihedral are considered. Solutions are presented for straight-tapered wings for a range of swept plan forms.
Date: December 22, 1949
Creator: DeYoung, John

Maneuverability investigation of an F6C-4 fighting airplane

Description: "In order to compare the relative maneuverability of two fighting airplanes and to accumulate additional data to assist in establishing a satisfactory criterion for the maneuverability of any airplane, the National Advisory Committee for Aeronautics has conducted maneuverability investigations on the F6C-3 (water-cooled engine) and the F6C-4 (air-cooled engine) airplanes. The investigation made on the F6C-3 airplane was reported in NACA-TR-369. This report contains the results of the investigation made on the F6C-4 airplane" (p. 475).
Date: December 12, 1930
Creator: Dearborn, C. H. & Kirschbaum, H. W.

Calculation of the aerodynamic loading of swept and unswept flexible wings of arbitrary stiffness

Description: A method is presented for calculating the aerodynamic loading, the divergence speed, and certain stability derivatives of swept and unswept wings and tail surfaces of arbitrary stiffness. Provision is made for using either stiffness curves and root rotation constants or structural influence coefficients in the analysis. Computing forms, tables of numerical constants required in the analysis, and an illustrative example are included to facilitate calculations by means of the method.
Date: December 24, 1948
Creator: Diederich, Franklin W.

Matrix method of determining the longitudinal-stability coefficients and frequency response of an aircraft from transient flight data

Description: From Summary: "A matrix method is presented for determining the longitudinal-stability coefficients and frequency response of an aircraft from arbitrary maneuvers. The method is devised so that it can be applied to time-history measurements of combinations of such simple quantities as angle of attack, pitching velocity, load factor, elevator angle, and hinge moment to obtain the over-all coefficients. Although the method has been devised primarily for the evaluation of stability coefficients which are of primary interest in most aircraft loads and stability studies, it can be used also, with a simple additional computation, to determine the frequency-response characteristics. The entire procedure can be applied or extended to other problems which can be expressed by linear differential equations."
Date: December 15, 1950
Creator: Donegan, James J. & Pearson, Henry A.

One-Dimensional Flows of an Imperfect Diatomic Gas

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" (p. 239).
Date: December 30, 1948
Creator: Eggers, A. J., Jr.

Bodies of revolution having minimum drag at high supersonic airspeeds

Description: Approximate shapes of nonlifting bodies having minimum pressure foredrag at high supersonic airspeeds are calculated. With the aid of Newton's law of resistance, the investigation is carried out for various combinations of the conditions of given body length, base diameter, surface area, and volume. In general, it is found that when body length is fixed, the body has a blunt nose; whereas, when the length is not fixed, the body has a sharp nose. The additional effect of curvature of the flow over the surface is investigated to determine its influence on the shapes for minimum drag. The effect is to increase the bluntness of the shapes in the region of the nose and the curvature in the region downstream of the nose. These shape modifications have, according to calculation, only a slight tendency to reduce drag. Several bodies of revolution of fineness ratios 3 and 5, including the calculated shapes of minimum drag for given length and base diameter and for given base diameter and surface area, were tested at Mach numbers from 2.73 to 6.28. A comparison of theoretical and experimental foredrag coefficients indicates that the calculated minimum-drag bodies are reasonable approximations to the correct shape.
Date: December 14, 1955
Creator: Eggers, A. J., Jr.; Resnikoff, Meyer M. & Dennis, David H.

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

Description: From Summary: "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."
Date: December 10, 1954
Creator: Eggers, Alfred J., Jr.; Allen, H. Julian & Neice, Stanford E.

Effect of ground interference on the aerodynamic and flow characteristics of a 42 degree sweptback wing at Reynolds numbers up to 6.8 x 10(6)

Description: Report presents the results of an investigation of the effects of ground interference on the aerodynamic characteristics of a 42 degree sweptback wing at distances 0.68 and 0.92 of the mean aerodynamic chord from the simulated ground to the 0.25-chord point of the mean aerodynamic chord. Survey data behind the wing, both with and without the simulated ground, are presented in the form of contour charts of downwash, sidewash, and dynamic-pressure ratio at longitudinal stations of 2.0 and 2.8 mean aerodynamic chords behind the wing.
Date: December 17, 1954
Creator: Furlong, G. Chester & Bollech, Thomas V.

Preliminary flight tests of the N.A.C.A. Roots type aircraft engine supercharger

Description: "An investigation of the suitability of the N.A.C.A. Roots type aircraft engine supercharger to flight-operating conditions, as determined the effects of the use of the supercharger upon engine operation and airplane performance, is described in this report. Attention was concentrated on the operation of the engine-supercharger unit and on the improvement of climbing ability; some information concerning high speeds at altitude was obtained. The supercharger was found to be satisfactory under flight-operating conditions. Although two failures occurred during the tests, the causes of both were minor and have been eliminated" (p. 207).
Date: December 29, 1926
Creator: Gardiner, Arthur W. & Reid, Elliott G.

Bending-torsion flutter calculations modified by subsonic compressibility corrections

Description: From Summary: "A number of calculations of bending-torsion wing flutter are made at two Mach numbers, m=0 (incompressible case) and m=0.7, and results are compared. The air forces employed for the case of m=0.7 are based on Frazer's recalculation of Possio's results, which are derived on the assumption of small disturbances to the main flow. For ordinary wings of normal density and of low bending frequency in comparison with torsion frequency, the compressibility correction to the flutter speed appears to be of the order of a few percent; whereas the correction to flutter speed for high-density wing sections, such as propeller sections, and to the wing-divergence speed in general, may be based on a rule using the (1 - m(2))1/4 factor and, for m=0.7, represents a decrease of the order of 17 percent."
Date: December 18, 1945
Creator: Garrick, I. E.

Experimental and analytical determination of the motion of hydraulically operated valve stems in oil engine injection systems

Description: This research on the pressure variations in the injection system of the N.A.C.A. Spray Photography Equipment and on the effects of these variations on the motion of the timing valve stem was undertaken in connection with the study of fuel injection systems for high-speed oil engines. The methods of analysis of the pressure variations and the general equation for the motion of the spring-loaded stem for the timing valve are applicable to a spring-loaded automatic injection valve, and in general to all hydraulically operated valves. A sample calculation for a spring-loaded automatic injection valve is included.
Date: December 26, 1928
Creator: Gelalles, A. G. & Rothrock, A. M.

Measurement of Static Pressure on Aircraft

Description: "Existing data on the errors involved in the measurement of static pressure by means of static-pressure tubes and fuselage vents are presented. The errors associated with the various design features of static-pressure tubes are discussed for the condition of zero angle of attack and for the case where the tube is inclined to flow. Errors which result from variations in the configuration of static-pressure vents are also presented" (p. 645).
Date: December 17, 1956
Creator: Gracey, William

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

Description: From Introduction: "The present paper is restricted to a discussion of wing theory subject to the assumptions of linearized compressible flow. It therefore employs solutions of Laplace's equation and the wave equation for cases where the boundary condition are specified in the plane of the wing."
Date: December 22, 1948
Creator: Heaslet, Max A. & Lomax, Harvard

Two-dimensional unsteady lift problems in supersonic flight

Description: The variation of pressure distribution is calculated for a two-dimensional supersonic airfoil either experiencing a sudden angle-of-attack change or entering a sharp-edge gust. From these pressure distributions the indicial lift functions applicable to unsteady lift problems are determined for two cases. Results are presented which permit the determination of maximum increment in lift coefficient attained by an unrestrained airfoil during its flight through a gust. As an application of these results, the minimum altitude for safe flight through a specific gust is calculated for a particular supersonic wing of given strength and wing loading.
Date: December 5, 1947
Creator: Heaslet, Max A. & Lomax, Harvard

Linearized compressible-flow theory for sonic flight speeds

Description: The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author).
Date: December 12, 1948
Creator: Heaslet, Max A.; Lomax, Harvard & Spreiter, John R.