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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
An investigation was made to determine a method of measuring fuel-air ratio that could be used for test purposes in flight and for checking conventional equipment in the laboratory. Two single-cylinder test engines equipped with typical commercial engine cylinders were used. The fuel-air ratio of the mixture delivered to the engines was determined by direct measurement of the quantity of air and of fuel supplied and also by analysis of the oxidized exhaust gas and of the normal exhaust gas. Five fuels were used: gasoline that complied with Army-Navy Fuel Specification, No. AN-VV-F-781 and four mixtures of this gasoline with toluene, benzene, and xylene. The method of determining the fuel-air ratio described in this report involves the measurement of the carbon-dioxide content of the oxidized exhaust gas and the use of graphs or the presented equation. This method is considered useful in aircraft, in the field, or in the laboratory for a range of fuel-air ratios from 0.047 to 0.124.
Recent airfoil data for both flight and wind-tunnel tests have been collected and correlated insofar as possible. The flight data consist largely of drag measurements made by the wake-survey method. Most of the data on airfoil section characteristics were obtained in the Langley two-dimensional low-turbulence pressure tunnel. Detail data necessary for the application of NACA 6-serles airfoils to wing design are presented in supplementary figures, together with recent data for the NACA 24-, 44-, and 230-series airfoils. The general methods used to derive the basic thickness forms for NACA 6- and 7-series airfoils and their corresponding pressure distributions are presented. Data and methods are given for rapidly obtaining the approximate pressure distributions for NACA four-digit, five-digit, 6-, and 7-series airfoils. The report includes an analysis of the lift, drag, pitching-moment, and critical-speed characteristics of the airfoils, together with a discussion of the effects of surface conditions. Available data on high-lift devices are presented. Problems associated with lateral-control devices, leading-edge air intakes, and interference are briefly discussed. The data indicate that the effects of surface condition on the lift and drag characteristics are at least as large as the effects of the airfoil shape and must be considered in airfoil selection and the prediction of wing characteristics. Airfoils permitting extensive laminar flow, such as the NACA 6-series airfoils, have much lower drag coefficients at high speed and cruising lift coefficients than earlier types-of airfoils if, and only if, the wing surfaces are sufficiently smooth and fair. The NACA 6-series airfoils also have favorable critical-speed characteristics and do not appear to present unusual problems associated with the application of high-lift and lateral-control devices. Much of the data given in the NACA Advance Confidential Report entitled "Preliminary Low-Drag-Airfoil and Flap Data from Tests at Large Reynolds Number and Low Turbulence," by Eastman N. ...
Symbols and definition of various airspeed terms that have been adopted as standard by the NACA subcommittee on aircraft structural design are presented. The equations, charts, and tables required in the evaluation of true airspeed, calibrated airspeed, equivalent airspeed, impact and dynamic pressures, and Mach and Reynolds numbers have been compiled. Tables of the standard atmosphere to an altitude of 65,000 feet and a tentative extension to an altitude of 100,000 feet are given along with the basic equations and constants on which both the standard atmosphere and the tentative extension are based.
Statistical measurements of contact conditions have been obtained, by means of a special photographic technique, of 478 landings of present-day transport airplanes made during routine daylight operations in clear air at the Washington National Airport. From the measurements, sinking speeds, rolling velocities, bank angles, and horizontal speeds at the instant before contact have been evaluated and a limited statistical analysis of the results has been made and is reported in this report.
An investigation was made to determine the accuracy with which the lateral flight motions of a swept-wing airplane could be predicted from experimental stability derivatives, determined in the 6-foot-diameter rolling-flow test section and 6 by 6-foot curved-flow test section of the Langley stability tunnel. In addition, determination of the significance of including the nonlinear aerodynamic effects of sideslip in the calculations of the motions was desired. All experimental aerodynamic data necessary for prediction of the lateral flight motions are presented along with a number of comparisons between flight and calculated motions caused by rudder and aileron disturbances.
Comparisons have been made of the shock phenomena and drag-rise increments for representative wing and central-body combinations with those for bodies of revolution having the same axial developments of cross-sectional areas normal to the airstream. On the basis of these comparisons, it is concluded that near the speed of sound the zero-lift drag rise of a low-aspect-ratio thin-wing and body combination is primarily dependent on the axial development of the cross-sectional areas normal to the airstream. It follows that the drag rise for any such configuration is approximately the same as that for any other with the same development of cross-sectional areas. Investigations have also been made of representative wing-body combinations with the body so indented that the axial developments of cross-sectional areas for the combinations were the same as that for the original body alone. Such indentations greatly reduced or eliminated the zero-lift drag-rise increments associated with the wings near the speed of sound.
The effect of several parameters on the drag characteristics of practical-construction wing sections have been considered and evaluated. The effects considered were those of surface roughness, surface waviness, compressive load, and de-icers. The data were obtained from a number of tests in the Langley two-dimensional low-turbulence tunnels.
A summary has been made of available data on the characteristics of airfoil sections with trailing-edge high-lift devices. Data for plain, split, and slotted flaps are collected and analyzed. The effects of each of the variables involved in the design of the various types of flap are examined and, in cases where sufficient data are given, optimum configurations are deduced. Wherever possible, the effects of airfoil section, Reynolds number, and leading-edge roughness are shown. For single and double slotted flaps, where a large amount of unrelated data are available, maximum lift coefficients of many configurations are presented in tables.
Principles for designing the optimum hull for a large long-range flying boat to meet the requirements of seaworthiness, minimum drag, and ability to take off and land at all operational gross loads were incorporated in a 1/12-size powered dynamic model of a four-engine transport flying boat having a design gross load of 165,000 pounds. These design principles included the selection of a moderate beam loading, ample forebody length, sufficient depth of step, and close adherence to the form of a streamline body. The aerodynamic and hydrodynamic characteristics of the model were investigated in Langley tank no. 1. Tests were made to determine the minimum allowable depth of step for adequate landing stability, the suitability of the fore-and-aft location of the step, the take-off performance, the spray characteristics, and the effects of simple spray-control devices. The application of the design criterions used and test results should be useful in the preliminary design of similar large flying boats.
A single-stage axial fan was built and tested in the shop of the propeller-research tunnel of the NACA. The fan comprised a simple 24-blade rotor having a diameter of 21 inches and a solidity of 0.86 and a set of 37 contravanes having a solidity of 1.33. The rotor was driven by a 25-horsepower motor capable of rotating at a speed of 3600 r.p.m. The fan was tested for volume, pressure, and efficiency over a range of delivery pressures and volumes for a wide range of contravane and blade-angle settings. The test results are presented in chart form in terms of nondimensional units in order that similar fans may be accurately designed with a minimum effort. The maximum efficiency (88 percent) was obtained by the fan at a blade angle of 30 degrees and a contravane angle of 70 degrees. An efficiency of 80 percent was obtained by the fan with the contravanes removed.
A method is presented for determining the effect of time lag in an automatic stabilization system on the lateral oscillatory stability of an airplane. The method is based on an analytical-graphical procedure. The critical time lag of the airplane-autopilot system is readily determined from the frequency-response analysis. The method is applied to a typical present-day airplane equipped with an automatic pilot sensitive to yawing acceleration and geared to the rudder so that rudder control is applied in proportion to the yawing acceleration. The results calculated for this airplane-autopilot system by this method are compared with the airplane motions calculated by a step-by-step procedure.
The general equations of motion for an airplane with a number of spherical fuel tanks are derived. The motion of the fuel is approximated by the motion of solid pendulums. The same type of derivation and equations are shown to apply to any type of fuel tank where the motion of the fuel may be represented in terms of undamped harmonic oscillators. Motions are calculated for a present-day high-speed airplane and a free-flying airplane model with two spherical tanks in the symmetry plane.
The results of elevated-temperature compressive strength and creep tests of 2024-t3 (formerly 24s-t3) aluminum alloy plates supported in v-grooves are presented. The strength-test results indicate that a relation previously developed for predicting plate compressive strength for plates of all materials at room temperature is also satisfactory for determining elevated-temperature strength. Creep-lifetime results are presented for plates in the form of master creep-lifetime curves by using a time-temperature parameter that is convenient for summarizing tensile creep-rupture data. A comparison is made between tensile and compressive creep lifetime for the plates and a method that made use of isochronous stress-strain curves for predicting plate-creep failure stresses is investigated.
The bending stresses in the covers of box beams or wide-flange beams differ appreciably from the stresses predicted by the ordinary bending theory on account of shear deformation of the flanges. The problem of predicting these differences has become known as the shear-lag problem. The first part of this paper deals with methods of shear-lag analysis suitable for practical use. The second part of the paper describes strain-gage tests made by the NACA to verify the theory. Three tests published by other investigators are also analyzed by the proposed method. The third part of the paper gives numerical examples illustrating the methods of analysis. An appendix gives comparisons with other methods, particularly with the method of Ebner and Koller.
A theoretical investigation has been made to determine the effect of nonlinear stability derivatives on the lateral stability of an airplane. Motions were calculated on the assumption that the directional-stability and the damping-in-yawing derivatives are functions of the angle of sideslip. The application of the Laplace transform to the calculation of an airplane motion when certain types of nonlinear derivatives are present is described in detail. The types of nonlinearities assumed correspond to the condition in which the values of the directional-stability and damping-in-yawing derivatives are zero for small angle of sideslip.
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.
An Army liaison-type airplane, representative of personal airplanes in the 150 to 200 horsepower class, has been modified to reduce propeller and engine noise according to known principles of airplane-noise reduction. Noise-level measurements demonstrate that, with reference to an observer on the ground, a noisy airplane of this class can be made quiet -- perhaps more quiet than necessary. In order to avoid extreme and unnecessary modifications, acceptable noise levels must be determined.
Report presents the results of sound measurements at static conditions made for a two-blade 47-inch-diameter propeller in the tip Mach number range 0.75 to 1.30. For comparison, spectrums have been obtained at both subsonic and supersonic tip speeds. In addition, the measured data are compared with calculations by the theory of Gutin which has previously been found adequate for predicting the sound at subsonic tip speeds. Curves are presented from which the maximum over-all noise levels in free space may be estimated if the power, tip Mach number, and distance are known.
Theoretical studies have predicted that operation of helicopter rotor beyond certain combinations of thrust, forward speed, and rotational speed might be prevented by rapidly increasing stalling of the retreating blade. The same studies also indicate that the efficiency of the rotor will increase until these limits are reached or closely approached, so that it is desirable to design helicopter rotors for operation close to the limits imposed by blade stalling. Inasmuch as the theoretical predictions of blade stalling involve numerous approximations and assumptions, an experimental investigation was needed to determine whether, in actual practice, the stall did occur and spread as predicted and to establish the amount of stalling that could be present without severe vibration or control difficulties being introduced. This report presents the results of such an investigation.
Instrument-flying trials have been conducted in a single-rotor helicopter, the maneuver stability of which could be changed from satisfactory to unsatisfactory. The results indicated that existing longitudinal flying-qualities requirements based on contact flight were adequate for instrument flight at speeds above that for minimum power. However, lateral-directional problems were encountered at low speeds and during precision maneuvers. The adequacy, for helicopter use, of standard airplane instruments was also investigated, and the conclusion was reached that special instruments would be desirable under all conditions, and necessary for sustained low-speed instrument flight.
A procedure is presented for obtaining the pressure distribution on an arbitrary airfoil section in cascade in a two-dimensional, incompressible, and nonviscous flow. The method considers directly the influence on a given airfoil of the rest of the cascade and evaluates this interference by an iterative process, which appeared to converge rapidly in the cases tried (about unit solidity, stagger angles of 0 degree and 45 degrees). Two variations of the basic interference calculations are described. One, which is accurate enough for most purposes, involves the substitution of sources, sinks, and vortices for the interfering airfoils; the other, which may be desirable for the final approximation, involves a contour integration. The computations are simplified by the use of a chart presented by Betz in a related paper. Illustrated examples are included.
Report presents the results of an investigation conducted in the Langley propeller research tunnel to study cowling-spinner combinations based on the NACA 1-series nose inlets and to obtain systematic design data for one family of approximately ellipsoidal spinners. In the main part of the investigation, 11 of the related spinners were tested in various combinations with 9 NACA open-nose cowlings, which were also tested without spinners. The effects of location and shape of the spinner, shape of the inner surface of the cowling lip, and operation of a propeller having approximately oval shanks were investigated briefly. In addition, a study was conducted to determine the correct procedure for extrapolating design conditions determined from the low-speed test data to the design conditions at the actual flight Mach number.
The results of pressure-distribution and force tests of four wings at a Mach number of about 6.9 and a Reynolds number of 0.98 x 10(6) in the Langley 11-inch hypersonic tunnel are presented. The wings had a square plan form, a 5-percent-chord maximum thickness, and diamond, half-diamond, wedge, and half-circular sections.
The results of measurements in the Langley full-scale tunnel of the maximum lift coefficients and stalling characteristics of airplanes have been collected. The data have been analyzed to show the nature of the effects on maximum lift and stall of wing geometry, fuselages and nacelles, propeller slipstream, surface roughness, and wing leading-edge appendages such as ducts, armaments, tip slats, and airspeed heads. Comparisons of full-scale-tunnel and flight measurements of maximum lift and stall are included in some cases, and the effects of the different testing techniques on the maximum-lift measurements are also given.
Report presents the results of force tests made of a 1/8-scale model of a twin-engine low-wing transport airplane in the NACA 8-foot high-speed tunnel to investigate compressibility and interference effects of speeds up to 450 miles per hour. In addition to tests of the standard arrangement of the model, tests were made with several modifications designed to reduce the drag and to increase the critical speed.
The drag characteristics of eight radial-engine cowlings have been determined over a wide speed range in the NACA 8-foot high-speed wind tunnel. The pressure distribution over all cowlings was measured, to and above the speed of the compressibility burble, as an aid in interpreting the force tests. One-fifth-scale models of radial-engine cowlings on a wing-nacelle combination were used in the tests.
Report presents the results of investigations conducted on a full-scale air-cooled aircraft-engine cylinder of 202-cubic inch displacement to determine the effects of internal cooling by water induction on the maximum permissible power and output of an internal-combustion engine. For a range of fuel-air and water-fuel ratios, the engine inlet pressure was increased until knock was detected aurally, the power was then decreased 7 percent holding the ratios constant. The data indicated that water was a very effective internal coolant, permitting large increases in engine power as limited by either knock or by cylinder temperatures.
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.
A method is presented for the calculation of the flutter speed of a uniform wing carrying an arbitrarily placed concentrated mass. The method, an extension of recently published work by Goland and Luke, involves the solution of the differential equations of motion of the wing at flutter speed and therefore does not require the assumption of specific normal modes of vibration. The order of the flutter determinant to be solved by this method depends upon the order of the system of differential equations and not upon the number of modes of vibration involved. The differential equations are solved by operational methods, and a brief discussion of operational methods as applied to boundary-value problems is included in one of two appendixes. A comparison is made with experiment for a wing with a large eccentrically mounted weight and good agreement is obtained. Sample calculations are presented to illustrate the method; and curves of amplitudes of displacement, torque, and shear for a particular case are compared with corresponding curves computed from the first uncoupled normal modes.
General formulas are given for propellers for the rate of change of side-force coefficient with angle of yaw and for the rate of change of pitching-moment coefficient with angle of yaw. Charts of the side-force derivative are given for two propellers of different plan form. The charts cover solidities of two to six blades and single and dual rotation. The blade angle ranges from 15 degrees or 20 degrees to 60 degrees.
The theory is given for calculating the free-space oscillating pressures associated with a rotating propeller, at any point in space. Because of its complexity this analysis is convenient only for use in the critical region near the propeller tips where the assumptions used by Gutin to simplify his final equations are not valid. Good agreement was found between analytical and experimental results in the tip Mach number range 0.45 to two, three, four, five, six, on eight-blade propellers and for a range of tip clearances from 0.04 to 0.30 times the propeller diameter. If the power coefficient, tip Mach number, and the tip clearance are known for a given propeller, the designer may determine from these charts the average maximum free-space oscillating pressure in the critical region near the plane of rotation. A section of the report is devoted to the fuselage response to these oscillating pressures and indicates some of the factors to be considered in solving the problems of fuselage vibration and noise.
A frequency-response method for determining the critical control-gearing and hunting oscillations of airplanes with automatic pilots is presented. The method is graphical and has several advantages over the standard numerical procedure based on Routh's discriminant. The chief advantage of the method is that direct use can be made of the measured response characteristics of the automatic pilot. This feature is especially useful in determining the existence, amplitude, and frequency of the hunting oscillations that may be present when the automatic pilot has nonlinear dynamic characteristics. Several examples are worked out to illustrate the application of the frequency-response method in determining the effect of automatic-pilot lag or lead on critical control gearing and in determining the amplitude and frequency hunting. It is shown that the method may be applied to the case of a control geared to airplane motions about two axes.
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