The load distribution, forces, and moments are calculated theoretically for inclined slender wing-body combinations consisting of a slender body of revolution and either a plane or cruciform arrangement of low-aspect-ratio pointed wings. The results are applicable at subsonic and transonic speeds, and at supersonic speeds, provided the entire wing-body combination lies near the center of the Mach cone.
Methods for computing spanwise blade-temperature distributions are derived for air-cooled hollow blades, air-cooled hollow blades with inserts, and air-cooled blades containing internal cooling fins. Individual and combined effects on spanwise blade-temperature distributions of cooling-air and radial heat conduction are determined. In general, the effects of radiation and radial heat conduction were found to be small and the omission of these variations permitted the construction of nondimensional charts for use in determining spanwise temperature distribution through air-cooled turbine blades. An approximate method for determining the allowable stress-limited blade-temperature distribution is included, with brief accounts of a method for determining the maximum allowable effective gas temperatures and the cooling-air requirements. Numerical examples that illustrate the use of the various temperature-distribution equations and of the nondimensional charts are also included.
Report includes the National Advisory Committee for Aeronautics letter of submittal to the President, summaries of the committee's activities and research accomplished, bibliographies, and financial report.
Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.
Basic general equations governing the three-dimensional compressible flow of gas through a compressor or turbine are given in terms of total enthalpy, entropy, and velocity components of the gas. Two methods of solution are obtained for the simplified, steady axially symmetric flow; one involves the use of a number of successive planes normal to the axis of the machine and short distances apart, and the other involves only three stations for a stage in which an appropriate radial-flow path is used. Methods of calculation for the limiting cases of zero and infinite blade aspect ratios and an approximate method of calculation for finite blade aspect ratio are also given. In these methods, the blade loading and the shape of the annular passage wall may be arbitrarily specified.
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 wing-tunnel tests. The report presents a summary and unification of the existing literature on the subject.
A method is developed consistent with the assumptions of small perturbation theory which provides a means of determining the downwash behind a wing in supersonic flow for a known load distribution. The analysis is based upon the use of supersonic doublets which are distributed over the plan form and wake of the wing in a manner determined from the wing loading. The equivalence in subsonic and supersonic flow of the downwash at infinity corresponding to a given load distribution is proved.
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.
Signal Corps wind equipment AN/GMQ-1 consisting of a 3-cup anemometer and wind vane was calibrated for wind velocities from 1 to 200 miles per hour. Cup-shaft failure prevented calibration at higher wind velocities. The action of the wind vane was checked and found to have very poor directional accuracy below a velocity of 8 miles per hour. After shaft failure was reported to the Signal Corps, the cup rotors were redesigned by strengthening the shafts for better operation at high velocities. The anemometer with the redesigned cup rotors was recalibrated, but cup-shaft failure occurred again at a wind velocity of approximately 220 miles per hour. In the course of this calibration two standard generators were checked for signal output variation, and a wind-speed meter was calibrated for use with each of the redesigned cup rotors. The variation of pressure coefficient with air-flow direction at four orifices on a disk-shaped pitot head was obtained for wind velocities of 37.79 53.6, and 98.9 miles per hour. A pitot-static tube mounted in the nose of a vane was calibrated up to a dynamic pressure of 155 pounds per square foot, or approximately 256 miles per hour,.
Directly comparable drag measurements have been made of an airfoil with a conventional rectangular plan form and an airfoil with a sweptback plan form mounted on freely falling bodies. Both airfoils had NACA 65-009 sections and were identical in span, frontal area, and chord perpendicular to the leading edge. The sweptback plan form incorporated a sweepback angle of 45 degrees. The data obtained have been used to establish the relation between the airfoil drag coefficients and the free-stream Mach number over a range of Mach numbers from 0.90 to 1.27. The results of the measurements indicate that the drag of the sweptback plan form is less than 0.3 that of the rectangular plan form at a Mach number of 1.00 and is less than 0.4 that at a Mach number of 1.20.
A chart in terms of nondimensional parameters is presented for the theoretical critical stress in torsion of simply supported cylinders stiffened by identical equally spaced rings of zero torsional stiffness. The results are obtained by solving the equation of equilibrium by means of the Galerkin method. Comparison of the theoretical results with experimental results indicates that ring-stiffened cylinders buckle, on the average, at a buckling stress about 15 percent below the theoretical buckling stress. (author).
The results of local-instability tests of h-section plate assemblies and compressive stress-strain tests of extruded 75s-t6 aluminum alloy, obtained to determine flat-plate compressive strength under stabilized elevated temperature conditions, are given for temperatures up to 600 degrees F. The results show that methods available for calculating the critical compressive stress at room temperature can also be used at elevated temperatures if the applicable compressive stress-strain curve for the material is given.
A method is presented for the determination of the contour of disks, typified by those of aircraft gas turbines, to incorporate arbitrary elastic-stress distributions resulting from either centrifugal or combined centrifugal and thermal effects. The specified stress may be radial, tangential, or any combination of the two. Use is made of the finite-difference approach in solving the stress equations, the amount of computation necessary in the evolution of a design being greatly reduced by the judicious selection of point stations by the aid of a design chart. Use of the charts and of a preselected schedule of point stations is also applied to the direct problem of finding the elastic and plastic stress distribution in disks of a given design, thereby effecting a great reduction in the amount of calculation. Illustrative examples are presented to show computational procedures in the determination of a new design and in analyzing an existing design for elastic stress and for stresses resulting from plastic flow.
An investigation of a 1/14-scale dynamically similar model of the Northrop C-125 airplane was made to determine the ditching characteristics and proper ditching technique for the airplane. Various conditions of damage, landing attitude, flap setting, and speed were investigated. The behavior of the model was determined from visual observations, motion-picture records, and time-history deceleration records. The results of the investigation are presented in table form, photographs, and curves. It was concluded that the airplane should be ditched at a nose-high landing attitude (near 8 deg) with flaps full down. The fixed landing gear will cause the airplane to dive. The fuselage will be damaged and will probably flood rapidly. Longitudinal decelerations will be about 4g and the length of landing run will be about two fuselage lengths. If the main landing gear could be jettisonable or retractable the ditching characteristics would be greatly improved.
A ditching investigation of a model of the Convair-Liner airplane was made to observe the behavior and determine the safest procedure for making an emergency water landing. The ditching model was designed and constructed by the National Advisory Committee for Aeronautics. Design information on the airplane was furnished by the Consolidated Vultee Aircraft Corporation. A three-view drawing of the airplane is shown. The investigation was made in calm water at the Langley tank no. 2 monorail.
An analysis is presented of the effect of torsional flexibility on the rolling characteristics at supersonic speeds of tapered unswept wings with partial-span constant-percent-chord ailerons extending inboard from the wing tip. The geometric variables considered are aspect ratio, taper ratio, aileron span, and aileron chord. The shape of the wing-torsional-stiffness curve is assumed and the twisting moment is considered to result solely from the pressure distribution caused by aileron deflection, so that the necessity of using a successive-approximation method is avoided. Because of the complexity of the equations resulting from the analysis, numerical calculations from the equations are presented in a series of figures. A computational form is provided to be used in conjunction with these figures so that calculations can be made without reference to the analysis.
Results are presented of an investigation made to determine the two-dimensional lift and drag characteristics of nine NACA 6-series airfoil section at Reynolds numbers of 15.0 x 10sub6, 20.0 x 10sub6, and 25.0 x 10sub6. Also presented are data from NACA Technical Report 824 for the same airfoils at Reynolds numbers of 3.0 x 10sub6, 6.0 x 10sub6, and 9.0 x 10sub6. The airfoils selected represent sections having variations in the airfoil thickness, thickness form, and camber. The characteristics of an airfoil with a split flap were determined in one instance, as was the effect of surface roughness. Qualitative explanations in terms of flow behavior are advanced for the observed types of scale effect.
A solution is presented for the problem of the compressive buckling of simply supported, flat, rectangular, solid-core sandwich plates stressed either in the elastic range or in the plastic range. Charts for the analysis of long sandwich plates are presented for plates having face materials of 24s-t3 aluminum alloy, 76s-t6 alclad aluminum alloy, and stainless steel. A comparison of computed and experimental buckling stresses of square solid-core sandwich plates indicates fair agreement between theory and experiment.
In considering the motion of the rocket, at each instant of time only the state of those material particles which a t that instant are within the control surface passing through the exterior surface of the body of the rocket and the exit section of the nozzle shall be included. In order t o obtain the equations of motion of the rocket, the following procedure is used. An arbitrary but fixed instant of time is considered. A fictitious solid body is denoted by S with mass m, which would be obtained if the rocket at the instant t solidified and ceased giving off particles. The solid body S will not be homogeneous; in some of its parts, it will have the density of a metal and in other parts the density of a gas, and so forth. It shall be assumed that the fictitious solid body S is invariably fixed to the body of the rocket and from the instant t onwards (instant of solidification) moves together with the rocket. The momentum of the body S shall be denoted by Q.
A method of predicting equilibrium operating performance of turbojet engines has been developed, with the assumption of simple model processes for the components. Results of the analysis are plotted in terms of dimensionless parameters comprising critical engine dimensions and over-all operating variables. This investigation was made of an engine in which the ratio of axial inlet-air velocity to compressor-tip velocity is constant, which approximates turbojet engines with axial-flow compressors. Experimental correlation of the theory with data from several existing axial-flow-type engines was good and showed close correlation between calculated and measured performance.
A flight investigation was made to determine the effect of various vertical-tail modifications and of some combinations of these modifications on the directional stability and control characteristics of a propeller-driven fighter airplane. Six different vertical-tail configurations were investigated to determine the lateral-directional oscillation characteristics, the sideslip characteristics, the yaw due to ailerons in rudder-fixed rolls from turns and pull-outs, the trim changes due to speed changes, and the tim changes due to power changes. Results of the tests showed that increasing the aspect ratio of the vertical tail by 40 percent while increasing the area by only 12 percent approximately doubled the directional stability of the airplane. The pilots considered the directional characteristics of the airplane unsatisfactory with original vertical tail but satisfactory with the enlarged vertical tail. The ventral and dorsal fins tested had little effect on the directional stability of the airplane but were effective in eliminating rudder-force reversals in high-engine-power sideslips.
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.
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.
Methods are presented that use general correlative time-response input and output data for a linear system to determine the frequency-response function of that system. These methods give an exact description of any linear system for which such transient data are available. Examples are shown of application of a method to both an underdamped and a critically damped exact second-order system, and to an exact first-order system with and without dead time. Experimental data for a turbine-propeller engine showing the response of engine speed to change in propeller-blade angle are presented and analyzed.
A method is developed whereby the fundamental mechanisms are investigated by which processing, heat treatment, and chemical composition control the properties of alloys at high temperatures. The method used metallographic examination -- both optical and electronic --studies of x-ray diffraction-line widths, intensities, and lattice parameters, and hardness surveys to evaluate fundamental structural conditions. Mechanical properties at high temperatures are then measured and correlated with these measured structural conditions. In accordance with this method, a study was made of the fundamental mechanism by which aging controlled the short-time creep and rupture properties of solution-treated low-carbon n-155 alloy at 1200 degrees F.
Measurements have been made of the mean-total-head and mean-temperature fields in a round turbulent jet with various initial temperatures. The results show that the jet spreads more rapidly as its density becomes lower than that of the receiving medium, even when the difference is not sufficiently great to cause dynamic-pressure function. Rough analytical considerations have given the same relative spread. The effective "turbulent Prandtl number" for a section of the fully developed jet was found to be equal to the true (laminar) Prandtl number within the accuracy measurement.
A general algebraic method of attack on the problem of controlling gas-turbine engines having any number of independent variables was utilized employing operational functions to describe the assumed linear characteristics for the engine, the control, and the other units in the system. Matrices were used to describe the various units of the system, to form a combined system showing all effects, and to form a single condensed matrix showing the principal effects. This method directly led to the conditions on the control system for noninteraction so that any setting disturbance would affect only its corresponding controlled variable. The response-action characteristics were expressed in terms of the control system and the engine characteristics. The ideal control-system characteristics were explicitly determined in terms of any desired response action.
An investigation has been made in the Langley gust tunnel with two identical airplane models approximating 1/40-scale models of the B-29, coupled in tandem with a boom so that the individual centers of gravity were equidistant from the single coupling joint at the tail of the lead airplane. Time histories of the boom joint load were obtained as the models were flown through a gust. The results indicate that on a similar configuration involving airplanes the size of B-29 airplanes a load on the boom joint of 10,000 to 14,000 pounds could be induced by encountering a gust of 50 feet per second and having a gradient distance of 17 chords, at a forward speed of 380 feet per second and that the total load is extremely sensitive to the steadiness of flight that can be maintained with or without a gust. It is felt that the results are probably satisfactory to show order of magnitude, but it does not appear possible that a precise determination of the joint load that would be applicable to the full-scale airplanes can be obtained by gust-tunnel tests.
Despite the development of relatively ice-free fuel-metering systems, the widespread use of alternate and heated-air intakes, and the use of alcohol for emergency de-icing, icing of aircraft-engine induction systems is a serious problem. Investigations have been made to study and to combat all phases of this icing problem. From these investigations, criterions for safe operation and for design of new induction systems have been established. The results were obtained from laboratory investigations of carburetor-supercharger combinations, wind-tunnel investigations of air scoops, multicylinder-engine studies, and flight investigations. Characteristics of three forms of ice, impact, throttling, and fuel evaporation were studied. The effects of several factors on the icing characteristics were also studied and included: (1) atmospheric conditions, (2) engine and air-scoop configurations, including light-airplane system, (3) type fuel used, and (4) operating variables, such as power condition, use of a manifold pressure regulator, mixture setting, carburetor heat, and water-alcohol injection. In addition, ice-detection methods were investigated and methods of preventing and removing induction-system ice were studied. Recommendations are given for design and operation with regard to induction-system design.
In order to provide engineers interested in rotating-wing aircraft, but with no specialized training in stability theory, some understanding of the factors that influence the flying qualities of the helicopter, an explanation is made of both the static stability and the stick-fixed oscillation in hovering and forward flight in terms of fundamental physical quantities. Three significant stability factors -- static stability with angle of attack, static stability with speed, and damping due to a pitching or rolling velocity -- are explained in detail.
A low-scale wind-tunnel investigation was conducted in rolling flow to determine the effects of aspect ratio and sweep (when varied independently) on the rolling stability derivatives for a series of untapered wings. The rolling-flow equipment of the Langley stability tunnel was used for the tests. The data of the investigation have been used to develop a method of accounting for the effects of the drag on the yawing moment due to rolling throughout the lift range.
A rocket-propelled model of the Mx-656 configuration has been flown through the Mach number range from 0.65 to 1.25. An analysis of the response of the model to rapid deflections of the horizontal tail gave information on the lift, drag, longitudinal stability and control, and longitudinal-trim change. The lift-coefficient range covered by the test was from -0.2 to 0,3 throughout most of the Mach number range, The model was statically and dynamically stable throughout the lift-coefficient and Mach number range of the test. At subsonic speeds the aerodynamic center moved f o m r d with increasing lift coefficient. The most forward position of the aerodynamic center was about 12,5 percent of the mean aerodynamic chord at a small positive lift coefficient and at a Mach number of about 0.84. A t supersonic speeds the aerodynamic center was well aft, varying from 33 to 39 percent of the mean aerodynamic chord at Mach numbers of 1.0 and 1.25, respectively. Transonic-trim change, as measured by the change in trim lift coefficient with Mach number at a constant t a i l setting, was of small magnitude (about 0.1 lift coefficient for zero tail setting). The zero-lift/drag coefficient increased about 0.042 in the region between a Mach number of 0.9 and 1.1.
As part of a general investigation of propellers at high forward speeds, tests of two 2-blade propellers having the NACA 4-(3)(8)-03 and NACA 4-(3)(8)-45 blade designs have been made in the Langley 8-foot high-speed tunnel through a range of blade angle from 20 degrees to 60 degrees for forward Mach numbers from 0.165 to 0.725 to establish in detail the changes in propeller characteristics due to compressibility effects. These propellers differed primarily only in blade solidity, one propeller having 50 percent and more solidity than the other. Serious losses in propeller efficiency were found as the propeller tip Mach number exceeded 0.91, irrespective of forward speed or blade angle. The magnitude of the efficiency losses varied from 9 percent to 22 percent per 0.1 increase in tip Mach number above the critical value. The range of advance ratio for peak efficiency decreased markedly with increase of forward speed. The general form of the changes in thrust and power coefficients was found to be similar to the changes in airfoil lift coefficient with changes in Mach number. Efficiency losses due to compressibility effects decreased with increase of blade width. The results indicated that the high level of propeller efficiency obtained at low speeds could be maintained to forward sea-level speeds exceeding 500 miles per hour.
The free turbulent mixing of a supersonic jet of Mach number 1.6 has been experimentally investigated. An interferometer, of which a description is given, was used for the investigation. Density and velocity distributions through the mixing zone have been obtained. It was found that there was similarity in distribution at the cross sections investigated and that, in the subsonic portion of the mixing zone, the velocity distribution fitted the theoretical distribution for incompressible flow. It was found that the rates of spread of the mixing zone both into the jet and into the ambient air were less than those of subsonic jets.
A theoretical investigation of the velocity profiles for laminar mixing of a high-velocity stream with a region of fluid at rest has been made assuming that the Prandtl number is unity. A method which involves only quadratures is presented for calculating the velocity profile in the mixing layer for an arbitrary value of the free-stream Mach number. Detailed velocity profiles have been calculated for free-stream Mach numbers of 0, 1, 2, 3, and 5. For each Mach number, velocity profiles are presented for both a linear and a 0.76-power variation of viscosity with absolute temperature. The calculations for a linear variation are much simpler than those for a 0.76-power variation. It is shown that by selecting the constant of proportionality in the liner approximation such that it gives the correct value for the viscosity in the high-temperature part of the mixing layer, the resulting velocity profiles are in excellent agreement with those calculated by a 0.76-power variation.
The perturbation field induced by a line vortex in a supersonic stream and the downwash behind a supersonic lifting surface are examined to establish approximate methods for determining the downwash behind supersonic wings. Lifting-lines methods are presented for calculating supersonic downwash. A bent lifting-line method is proposed for computing the downwash field behind swept wings. When applied to triangular wings with subsonic leading edges, this method gives results that, in general, are in good agreement with the exact linearized solution. An unbent lifting-line method (horseshoe-vortex system) is proposed for unswept wings. This method is applied to determine downwash behind rectangular wings with aspect ratios of 2 and 4. Excellent agreement with exact linearized theory is obtained for both aspect ratios by placing the lifting line at the 1/2-chord point. The use of lifting-lines therefore appears promising for obtaining estimates of the downwash behind supersonic wings.
In the first part, the boundary conditions for an open wind tunnel (incompressible flow) are examined with special reference to the effects of the closed entrance and exit sections. Basic conditions are that the velocity must be continuous at the entrance lip and that the velocities in the upstream and downstream closed portions must be equal. In the second part, solutions are derived for four types of two-dimensional open tunnels, including one in which the pressures on the two free surfaces are not equal. Numerical results are given for every case. In general, if the lifting element is more than half the tunnel height from the inlet, the boundary effect at the lifting element is the same as for an infinitely long open tunnel. In the third part, a general method is given for calculating the boundary effect in an open circular wind tunnel of finite jet length. Numerical results are given for a lifting element concentrate at a point on the axis.
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).
The longitudinal stability characteristics of elastic swept wings of high aspect ratio experiencing bending and torsional deformations are calculated for supersonic speed by the application of linearized lifting-surface theory. A parabolic wing deflection curve is assumed and the analysis is simplified by a number of structural approximations. The method is thereby limited in application to wings of high aspect ratio for which the root effects are small. Expressions for the lift, pitching-moment, and span load distribution characteristics are derived in terms of the elastic properties of the wing; namely, the design stress, the modulus of elasticity, the shearing modulus, and the maximum design load factor. The analysis applies to wings with leading edges swept behind the Mach lines. In all cases, however, the trailing edge is sonic or supersonic. Application of the method of analysis to wings with leading edges swept ahead of the Mach lines is discussed.
A method is presented for the determination of the frequency-response characteristics of an element or system by utilizing the transient output response to a known but arbitrary input to the system. Since the application of special inputs, such as step functions or sinusoids, is often imperfect or impractical, a method for utilizing arbitrary inputs is desirable. Simple flight-test data may be reduced by this method to give the frequency response of an aircraft. Examples are given as determinations of aircraft frequency responses; however, the method can be applied to any type of dynamic system, such as automatic-control components, vibration-absorption equipment, and many types of instruments. The method requires that the arbitrary input function tend to a finite value after a finite time and that the system or element output be measured as a representative quantity having a static sensitivity. (author).
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