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.
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.
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 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 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.
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.
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.
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.
With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author).
Flow-angle and pressure surveys behind five, thin, pointed-tip wings of varying plan form have been made at Mach numbers 1.62 and 2.41. Schlieren studies at a Mach number 1.93 for the same five plan-form wings were made to illustrate the behavior of the vortex sheet. The surveys were conducted at 1.5, 3, and 4 root chords behind three triangular wings of 50 degree, 63 degree, and 72 degree leading-edge sweep angle, and behind the 50 degree triangular wing reversed. The flow behind a pointed-tip wing having a sweptback leading edge and a sweptforward trailing edge (both 50 degrees) was also surveyed. Experiment and one of the theoretical methods are compared for the reversed triangular wing and the pointed-tip wing with the 50 degree sweptback leading edge and sweptforward trailing edge.
A wind-tunnel investigation was made to determine the effects on the aerodynamic characteristics of a 35 degree swept-wing airplane of applying area-suction boundary-layer control to the trailing-edge flaps. Flight tests of a similar airplane were then conducted to determine the effect of boundary-layer control in the handling qualities and operation of the airplane, particularly during landing. The wind-tunnel and flight tests indicated that area suction applied to the trailing-edge flaps produced significant increases in flap lift increment. Although the flap boundary-layer control reduced the stall speed only slightly, a reduction in minimum comfortable approach speed of about 12 knots was obtained.
A wind-tunnel investigation was made to determine the effects on the aerodynamic characteristics of a 35 degree swept-wing airplane of applying blowing-type boundary-layer control to the trailing-edge flaps. Flight tests of a similar airplane were then conducted to determine the effects of boundary-layer control on the handling qualities and operation of the airplane, particularly during landing and take-off. The wind-tunnel and flight tests indicated that blowing over the flaps produced large increases in flap lift increment, and significant increases in maximum lift. The use of blowing permitted reductions in the landing approach speeds of as much as 12 knots.
In a laboratory study of the factors involved in the influence of induction vacuum melting on 55ni-20cr-15co-4mo-3ti-3al heat resistant alloy, it was found that the major factor was the type of ceramic used as the crucible. The study concluded that trace amounts of boron or zirconium derived from reaction of the melt with the crucible refactories improved creep-rupture properties at 1,600 degrees F. Boron was most effective and, in addition, markedly improved hot-workability.
Flat 2024-t3 aluminum panels measuring 11 inches by 13 inches were tested in the near noise fields of a 4-inch air jet and turbojet engine. The stresses which were developed in the panels are compared with those calculated by generalized harmonic analysis. The calculated and measured stresses were found to be in good agreement. In order to make the stress calculations, supplementary data relating to the transfer characteristics, damping, and static response of flat and curved panels under periodic loading are necessary and were determined experimentally. In addition, an appendix containing detailed data on the near pressure field of the turbojet engine is included.
A large wind tunnel, approximately 8 feet in diameter, has been converted to transonic operation by means of slots in the boundary extending in the direction of flow. The usefulness of such a slotted wind tunnel, already known with respect to the reduction of the subsonic blockage interference and the production of continuously variable supersonic flows, has been augmented by devising a slot shape with which a supersonic test region with excellent flow quality could be produced. Experimental locations of detached shock waves ahead of axially symmetric bodies at low supersonic speeds in the slotted test section agreed satisfactorily with predictions obtained by use of existing approximate methods.
Long-range hypervelocity vehicles are studied in terms of their motion in powered flight. Powered flight is analyzed for an idealized propulsion system which approximates rocket motors. Unpowered flight is characterized by a return to earth along a ballistic, skip, or glide trajectory. Only those trajectories are treated which yield the maximum range for a given velocity at the end of powered flight. Aerodynamic heating is treated in a manner similar to that employed previously by the senior authors in studying ballistic missiles (NACA rep. 1381), with the exception that radiant as well as convective heat transfer is considered in connection with glide and skip vehicles. As a final performance consideration, it is shown that on the basis of equal ratios of mass at take-off to mass at the end of powered flight, the hypervelocity vehicle compares favorably with the supersonic airplane for ranges in the neighborhood of and greater than one half the circumference of the earth. In the light of this and previous findings, it is concluded that the ballistic and glide vehicles have, in addition to the advantages usually ascribed to great speed, the attractive possibility of providing relatively efficient long-range flight.
The equations are presented for the development of the compressible laminar boundary layer over a yawed infinite cylinder. For compressible flow with a pressure gradient the chordwise and spanwise flows are not independent. Using the Stewartson transformation and a linear viscosity-temperature relation yields a set of three simultaneous ordinary differential equations in a form yielding similar solutions. These equations are solved for stagnation-line flow for surface temperatures from zero to twice the free-stream stagnation temperature and for a wide range of yaw angle and free-stream Mach number. The results indicate that the effect of yaw on the heat-transfer coefficient at the stagnation line depends markedly on the free-stream Mach number. An unusual result of the solutions is that for large yaw angles and stream Mach numbers the chordwise velocity within the boundary layer exceeds the local external chordwise velocity, even for a highly cooled wall.
An analytical study of the effects of wing flexibility on wing strains due to gusts has been made for four spanwise stations of a four-engine bomber airplane, and the results have been correlated with results of a previous flight investigation.
The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper. Special attention is given the terms which are not included in previous theories. These terms are largely coupling-type terms associated with the centrifugal forces. Methods of solution of the equations of motion are indicated by selected examples.
Data from ditching investigations conducted at the Langley Aeronautical Laboratory with dynamic scale models of various airplanes are presented in the form of tables. The effects of design parameters on the ditching characteristics of airplanes, based on scale-model investigations and on reports of full-scale ditchings, are discussed. Various ditching aids are also discussed as a means of improving ditching behavior.
The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.
An analysis has been made to determine the effect of chord size on the weight and cooling characteristics of shell-supported, air-cooled gas-turbine blades. In uncooled turbines with solid blades, the general practice has been to design turbines with high aspect ratio (small blade chord) to achieve substantial turbine weight reduction. With air-cooled blades, this study shows that turbine blade weight is affected to a much smaller degree by the size of the blade chord.
Report presents the results of an investigation of the effects of fuel properties and of a number of fuel additives on combustion-chamber carbon deposition and exhaust-gas smoke formation in a single tubular turbojet-engine combustor. Limited tests were conducted with a number of the fuels in several full-scale turbojet engines to verify single-combustor data.
To help fill the gap in the knowledge of aerodynamics of shapes intermediate between bodies of revolution and flat triangular wings, force and moment characteristics for elliptic cones have been experimentally determined for Mach numbers of 1.97 and 2.94. Elliptic cones having cross-sectional axis ratios from 1 through 6 and with lengths and base areas equal to circular cones of fineness ratios 3.67 and 5 have been studied for angles of bank of 0 degree and 90 degrees. Elliptic and circular cones in combination with triangular wings of aspect ratios 1 and 1.5 also have been considered. The angle-of-attack range was from 0 degree to about 16 degrees, and the Reynolds number was 8 x 10(6), based on model length. In addition to the forces and moments at angle of attack, pressure distributions for elliptic cones at zero angle of attack have been determined. The results of this investigation indicate that there are distinct aerodynamic advantages to the use of elliptic cones.
Three wing models were oscillated in yaw about their vertical axes to determine the effects of systematic variations of frequency and amplitude of oscillation on the in-phase and out-of-phase combination lateral stability derivatives resulting from this motion. The tests were made at low speeds for a 60 degree delta wing, a 45 degree swept wing, and an unswept wing; the swept and unswept wings had aspect ratios of 4. The results indicate that large changes in the magnitude of the stability derivatives due to the variation of frequency occur at high angles of attack, particularly for the delta wing. The greatest variations of the derivatives with frequency take place for the lowest frequencies of oscillation; at the higher frequencies, the effects of frequency are smaller and the derivatives become more linear with angle of attack. Effects of amplitude of oscillation on the stability derivatives for delta wings were evident for certain high angles of attack and for the lowest frequencies of oscillation. As the frequency became high, the amplitude effects tended to disappear.
Various dummy stings were tested on the rear of a related series of afterbody shapes for Mach numbers from 0.80 to 1.10 and Reynolds numbers based on body length from 15.0 x 16 to the 6th power to 17.4 x 10 to the 6th power. A method is presented whereby approximate sting interference corrections can be made to models having afterbody shapes and sting supports similar to those of these tests if the Reynolds numbers are of the same order of magnitude and a turbulent boundary layer exists at the model base. Also presented is an analysis of jet duplication by use of a sting.
A number of noise-suppression nozzles were tested on full-scale engines. In general, these nozzles achieved noise reduction by the mixing interference of adjacent jets, that is, by using multiple-slot-nozzles. Several of the nozzles achieved reductions in sound power of approximately 5 decibels (nearly 70 percent) with small thrust losses (approx. 1 percent). The maximum sound-pressure level was reduced by as much as 18 decibels in particular frequency bands. Some of the nozzles showed considerable spatial asymmetry; that is, the sound field was not rotationally symmetrical. A method of calculating the limiting frequency effected by such nozzles is presented. Furthermore data are shown that appear to indicate that further reductions in sound power will not be easily achieved from nozzles using mixing interference as a means of noise suppression.
Report presents results of tests made on a power control system by means of a ground simulator to determine the effects of various combinations of valve friction and stick friction on the ability of the pilot to control the system. Various friction conditions were simulated with a rigid control system, a flexible system, and a rigid system having some backlash. For the tests, the period and damping of the simulated airplane were held constant.
Results are presented of an experimental and theoretical investigation of the growth of transverse velocity disturbances in the shear region caused by a flame in a duct. In the theoretical stability analysis, a flow field arising from a flame in a duct was analyzed. The flow was neutrally stable to symmetric disturbances and unstable to antisymmetric ones. In the experimental part of the program disturbances of various frequencies were imposed on a flame stabilized in a duct, and the effects were measured by shadow photography and photomultiplier-probe surveys.
This report gives the results of a detailed study of the flutter characteristics of four representative aircraft wings. This study was made using the electric-analog computer at the California Institute of Technology. During the course of this investigation eight important parameters of each wing were varied and, in addition, the effects of mass, inertia, pitching spring, and location of a concentrated mass were investigated for all four wings and at several sweepback angles.
A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.
Report presents the results of experimental and theoretical research conducted on flow separation associated with steps, bases, compression corners, curved surfaces, shock-wave boundary-layer reflections, and configurations producing leading-edge separation. Results were obtained from pressure-distribution measurements, shadowgraph observations, high-speed motion pictures, and oil-film studies. The maximum scope of measurement encompassed Mach numbers between 0.4 and 3.6, and length Reynolds numbers between 4,000 and 5,000,000.
For a body consisting of a fineness-ratio-3 ogival nose tangent to a cylindrical afterbody 7.3 diameters long, pitot-pressure distributions in the flow field, pressure distributions over the body, and downwash distributions along a line through the vortex centers have been measured for angles of attack to 20 degrees. The Reynolds numbers, based on body diameter, were 0.15 x 10 to the 6th power and 0.44 x 10 to the 6th power. Comparisons of computed and measured vortex paths and downwash distributions are made. (author).
Experimental drag measurements at zero angle of attack for various theoretical minimum drag nose shapes, hemispherically blunted cones, and other more common profiles of fineness ratios of about 3 are compared with theoretical results for a Mach number and Reynolds number range of 1.24 to 7.4 and 1.0 x 10 to the 6th power to 7.5 x 10 to the 6th power (based on body length), respectively. The results of experimental pressure-distribution measurements are used for the development of an empirical expression for predicting the pressure drag of hemispherically blunted cones.
An investigation was made in the Langley low-turbulence pressure tunnel to determine the effect of size and location of a sandpaper type of roughness on the Reynolds number for transition. Transition was observed by means of a hot-wire anemometer located at various chordwise stations for each position of the roughness. These observations indicated that when the roughness is sufficiently submerged in the boundary layer to provide a substantially linear variation of boundary-layer velocity with distance from the surface up to the top of the roughness, turbulent "spots" begin to appear immediately behind the roughness when the Reynolds number based on the velocity at the top of the roughness height exceeds a value of approximately 600. At Reynolds numbers even slightly below the critical value (value for transition), the sandpaper type of roughness introduced no measurable disturbances into the laminar layer downstream of the roughness. The extent of the roughness area does not appear to have an important effect on the critical value of the roughness Reynolds number.
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. Errors due to the position of a static-pressure tube in the flow field of the airplane are given for locations ahead of the fuselage nose, ahead of the wing tip, and ahead of the vertical tail fin. The errors of static-pressure vents on the fuselage of an airplane are also presented. Various methods of calibrating static-pressure installations in flight are briefly discussed.
In the course of a short flight program initiated to check the theory of Garrick and Watkins (NACA rep. 1198), a series of measurements at three stations were made of the oscillating pressures near a tapered-blade plan-form propeller and rectangular-blade plan form propeller at flight Mach numbers up to 0.72. In contradiction to the results for the propeller studied in NACA rep. 1198, the oscillating pressures in the plane ahead of the propeller were found to be higher than those immediately behind the propeller. Factors such as variation in torque and thrust distribution, since the blades of the present investigation were operating above their design forward speed, may account for this contradiction. The effect of blade plan form shows that a tapered-blade plan-form propeller will produce lower sound-pressure levels than a rectangular-blade plan-form propeller for the low blade-passage harmonics (the frequencies where structural considerations are important) and produce higher sound-pressure levels for the higher blade-passage harmonics (frequencies where passenger comfort is important).
"Thermal-gradient mass transfer" was investigated in the molten sodium hydroxide-nickel system. Possible mechanisms (physical, electrochemical, and chemical) are discussed in terms of experimental and theoretical evidence. Experimental details are included in appendixes.
It is demonstrated with the aid of similitude arguments that a model launched from a hypervelocity gun upstream through a special supersonic nozzle should experience aerodynamic heating and resulting thermal stresses like those encountered by a long-range ballistic missile entering the earth's atmosphere. This demonstration hinges on the requirements that model and missile be geometrically similar and made of the same material, and that they have the same flight speed and Reynolds number (based on conditions just outside the boundary layer) at corresponding points in their trajectories. The hypervelocity gun provides the model with the required initial speed, while the nozzle scales the atmosphere, in terms of density variation, to provide the model with speeds and Reynolds numbers over its entire trajectory. Since both the motion and aerodynamic heating of a missile tend to be simulated in the model tests, this combination of hypervelocity gun and supersonic nozzle is termed an atmosphere entry simulator.
A method of calculating the temperature of thick walls has been developed in which the time series and the response to a unit triangle variation of surface temperature concepts are used, together with essentially standard formulas for transient temperature and heat flow into thick walls. The method can be used without knowledge of the mathematical tools of its development. The method is particularly suitable for determining the wall temperature in one-dimensional thermal problems in aeronautics where there is a continuous variation of the heat-transfer coefficient and adiabatic-wall temperature. The method also offers a convenient means for solving the inverse problem of determining the heat-flow history when temperature history is known.
Part I of this report presents a brief review of methods available to the helicopter designer for obtaining desired stability characteristics by modifications to the airframe design. The discussion is based on modifications made during the establishment of flying-qualities criteria and includes sample results of theoretical studies of additional methods. The conclusion is reached that it is now feasible to utilize combinations of methods whereby stability-parameter values are realized which in turn provide the desired stability characteristics. Part II reviews some of the methods of predicting rotor stability derivatives. The procedures by which these rotor derivatives are employed to estimate helicopter stability characteristics have been summarized.
An extensive program was conducted to investigate the use of concentrated slurries of boron and magnesium in liquid hydrocarbon as fuels for afterburners and ramjet engines. Analytical calculations indicated that magnesium fuel would give greater thrust and that boron fuel would give greater range than are obtainable from jet hydrocarbon fuel alone. It was hoped that the use of these solid elements in slurry form would permit the improvement to be obtained without requiring unconventional fuel systems or combustors. Small ramjet vehicles fueled with magnesium slurry were flown successfully, but the test flights indicated that further improvement of combustors and fuel systems was needed.
The use of a magnetic field to control the motion of electrically conducting fluids is studied. The incompressible boundary-layer solutions are found for flow over a flat plate when the magnetic field is fixed relative to the plate or to the fluid. The equations are integrated numerically for the effect of the transverse magnetic field on the velocity and temperature profiles, and hence, the skin friction and rate of heat transfer. It is concluded that the skin friction and the heat-transfer rate are reduced when the transverse magnetic field is fixed relative to the plate and increased when fixed relative to the fluid. The total drag is increased in all of the areas.
The tendency for the jet engine rotor to continue to rotate after crash presents the probability that crash-spilled combustibles suspended in the air or puddled on the ground at the engine inlet may be sucked into the engine. Studies with jet engines operating on a test stand and full-scale crashes of turbojet-powered airplanes showed that combustibles drawn into the engine in this way ignite explosively within the engine. Experiment showed that the gas flow through the engine is too rapid to permit the ignition of ingested combustibles on the hot metal in contact with the main gas stream. Ignition will occur on those hot surfaces not in the main gas stream. The portion of the engine airflow is diverted for cooling and ventilation to these zones where the gas moves slowly enough for ignition to occur.
The statistical approach to the gust-load problem, which consists in considering flight through turbulent air to be a stationary random process, is extended by including the effect of lateral variation of the instantaneous gust intensity on the aerodynamic forces. The forces obtained in this manner are used in dynamic analyses of rigid and flexible airplanes free to move vertically, in pitch, and in roll. The effect of the interaction of longitudinal, normal, and lateral gusts on the wind stresses is also considered.
The similarity rules for linearized compressible flow theory (Gothert's rule and its supersonic counterpart) are extended to second order. It is shown that any second-order subsonic flow can be related to "nearly incompressible" flow past the same body, which can be calculated by the Janzen-Rayleigh method.
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