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**Decade:**1950-1959

**Serial/Series Title:**NACA Technical Reports

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

### Aerodynamic characteristics at high speeds of related full-scale propellers having different blade-section cambers

**Date:**1957?

**Creator:**Maynard, Julian D & Salters, Leland B , Jr

**Description:**Wind-tunnel tests of a full-scale two-blade NACA 10-(10)(08)-03 (high camber) propeller have been made for a range of blade angles from 20 degrees to 55 degrees at airspeeds up to 500 miles per hour. The results of these tests have been compared with results from previous tests of the NACA 10-(3) (08)-03 (low camber) and NACA 10-(5)(08)-03 (medium camber) propellers to evaluate the effects of blade-section camber on propeller aerodynamic characteristics.

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### Aerodynamic characteristics of a refined deep-step planing-tail flying-boat hull with various forebody and afterbody shapes

**Date:**1953

**Creator:**Riebe, John M & Naeseth, Rodger L

**Description:**An investigation was made in the Langley 300 mph 7-by 10-foot tunnel to determine the aerodynamic characteristics of a refined deep-step planing-tail hull with various forebody and afterbody shapes. For comparison, tests were made on a streamline body simulating the fuselage of a modern transport airplane. The results of the tests, which include the interference effects of a 21-percent-thick support wing, indicated that for corresponding configurations the hull models incorporating a forebody with a length-beam ratio of 7 had lower minimum drag coefficients than the hull models incorporating a forebody with a length-beam ratio of 5. Longitudinal and lateral stability was generally about the same for all hull models tested and about the same as that of a conventional hull.

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### Aerodynamic forces and loadings on symmetrical circular-arc airfoils with plain leading-edge and plain trailing-edge flaps

**Date:**1953

**Creator:**Cahill, Jones F; Underwood, William J; Nuber, Robert J & Cheesman, Gail A

**Description:**An investigation has been made in the Langley two-dimensional low-turbulence tunnel and in the Langley two-dimensional low-pressure tunnel of 6- and 10-percent-thick symmetrical circular-arc airfoil sections at low Mach numbers and several Reynolds numbers. The airfoils were equipped with 0.15-chord plain leading-edge flaps and 0.20-chord plan trailing-edge flaps. The section lift and pitching-moment characteristics were determined for both airfoils with the flaps deflected individually and in combination. The section drag characteristics were obtained for the 6-percent-thick airfoil with the flaps partly deflected as low-drag-control flaps and for airfoils with the flaps neutral. Surface pressures were measured on the 6-percent-thick airfoil section with the flaps deflected either individually or in appropriate combination to furnish flap load and hinge-moment data applicable to the structural design of the airfoil. A generalized method is developed that permits the determination of the chordwise pressure distribution over sharp-edge airfoils with plain leading-edge flaps and plain trailing-edge flaps of arbitrary size and deflection.

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### The aerodynamic forces on slender plane- and cruciform-wing and body combinations

**Date:**1950?~

**Creator:**Spreiter, John R

**Description:**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.

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### Air forces and moments on triangular and related wings with subsonic leading edges oscillating in supersonic potential flow

**Date:**1952?~

**Creator:**Watkins, Charles E & Berman, Julian N

**Description:**This analysis treats the air forces and moments in supersonic potential flow on oscillating triangular wings and a series of sweptback and arrow wings with subsonic leading edges and supersonic trailing edges. For the wings undergoing sinusoidal torsional oscillations simultaneously with vertical translations, the linearized velocity potential is derived in the form of a power series in terms of a frequency parameter. This method can be useful for treatment of similar problems for other plan forms and for wings undergoing other sinusoidal motions. For triangular wings, as many terms of such a series expansion as may be derived can be determined; however, the terms after the first few become very cumbersome. Closed expressions that include the reduced frequency to the fifth power, an order which is sufficient for a large class of practical application, are given for the velocity potential and for the components of chordwise section force and moment coefficients. These wings are found to exhibit the possibility of undamped torsional oscillations for certain ranges of Mach number and locations of the axis of rotation. The ranges of these parameters are delineated for triangular wings.

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### Airfoil profiles for minimum pressure drag at supersonic velocities -- general analysis with application to linearized supersonic flow

**Date:**January 1, 1952

**Creator:**Chapman, Dean R

**Description:**A theoretical investigation is made of the airfoil profile for minimum pressure drag at zero lift in supersonic flow. In the first part of the report a general method is developed for calculating the profile having the least pressure drag for a given auxiliary condition, such as a given structural requirement or a given thickness ratio. The various structural requirements considered include bending strength, bending stiffness, torsional strength, and torsional stiffness. No assumption is made regarding the trailing-edge thickness; the optimum value is determined in the calculations as a function of the base pressure. To illustrate the general method, the optimum airfoil, defined as the airfoil having minimum pressure drag for a given auxiliary condition, is calculated in a second part of the report using the equations of linearized supersonic flow.

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### Analog study of interacting and noninteracting multiple-loop control systems for turbojet engines

**Date:**January 1, 1955

**Creator:**Pack, George J & Phillips, W E , Jr

**Description:**The results of an analog investigation of several turbojet-engine control configurations is presented in this report. Both proportional and proportional-plus-integral controllers were studied, and compensating terms for engine interaction were added to the control system. Data were obtained on the stability limits and the transient responses of these various configurations. Analytical expressions in terms of the component transfer functions were developed for the configurations studied, and the optimum form for the compensation terms was determined. It was found that the addition of the integral term, while making the system slower and more oscillatory, was desirable in that it made the final values of the system parameters independent of source of disturbance and also eliminated droop in these parameters. Definite improvement in system characteristics resulted from the use of proper compensation terms. At comparable gain points the compensated system was faster and more stable. Complete compensation eliminated engine interaction, permitting each loop to be developed to an optimum point independently.

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### Analysis and calculation by integral methods of laminar compressible boundary-layer with heat transfer and with and without pressure gradient

**Date:**January 1, 1955

**Creator:**Morduchow, Morris

**Description:**A survey of integral methods in laminar-boundary-layer analysis is first given. A simple and sufficiently accurate method for practical purposes of calculating the properties (including stability) of the laminar compressible boundary layer in an axial pressure gradient with heat transfer at the wall is presented. For flow over a flat plate, the method is applicable for an arbitrarily prescribed distribution of temperature along the surface and for any given constant Prandtl number close to unity. For flow in a pressure gradient, the method is based on a Prandtl number of unity and a uniform wall temperature. A simple and accurate method of determining the separation point in a compressible flow with an adverse pressure gradient over a surface at a given uniform wall temperature is developed. The analysis is based on an extension of the Karman-Pohlhausen method to the momentum and the thermal energy equations in conjunction with fourth- and especially higher degree velocity and stagnation-enthalpy profiles.

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### An analysis of base pressure at supersonic velocities and comparison with experiment

**Date:**May 11, 1951

**Creator:**Chapman, Dean R

**Description:**In the first part of the investigation an analysis is made of base pressure in an inviscid fluid, both for two-dimensional and axially symmetric flow. It is shown that for two-dimensional flow, and also for the flow over a body of revolution with a cylindrical sting attached to the base, there are an infinite number of possible solutions satisfying all necessary boundary conditions at any given free-stream Mach number. For the particular case of a body having no sting attached only one solution is possible in an inviscid flow, but it corresponds to zero base drag. Accordingly, it is concluded that a strictly inviscid-fluid theory cannot be satisfactory for practical applications. An approximate semi-empirical analysis for base pressure in a viscous fluid is developed in a second part of the investigation. The semi-empirical analysis is based partly on inviscid-flow calculations.

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### An analysis of laminar free-convection flow and heat transfer about a flat plate paralled to the direction of the generating body force

**Date:**January 1, 1953

**Creator:**Ostrach, Simon

**Description:**The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.

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### Analysis of landing-gear behavior

**Date:**January 1, 1953

**Creator:**Milwitzky, Benjamin & Cook, Francis E

**Description:**This report presents a theoretical study of the behavior of the conventional type of oleo-pneumatic landing gear during the process of landing impact. The basic analysis is presented in a general form and treats the motions of the landing gear prior to and subsequent to the beginning of shock-strut deflection. The applicability of the analysis to actual landing gears has been investigated for the particular case of a vertical landing gear in the absence of drag loads by comparing calculated results with experimental drop-test data for impacts with and without tire bottoming. The calculated behavior of the landing gear was found to be in good agreement with the drop-test data.

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### Analysis of means of improving the uncontrolled lateral motions of personal airplanes

**Date:**January 1, 1951

**Creator:**Mckinney, Marion O , Jr

**Description:**A theoretical analysis has been made of means of improving the uncontrolled motions of personal airplanes. The purpose of this investigation was to determine whether such airplanes could be made to fly uncontrolled for an indefinite period of time without getting into dangerous attitudes and for a reasonable period of time (1 to 3 min) without deviating excessively from their original course. The results of this analysis indicated that the uncontrolled motions of a personal airplane could be made safe as regards spiral tendencies and could be greatly improved as regards maintenance of course without resort to an autopilot. The only way to make the uncontrolled motions completely satisfactory as regards continuous maintenance of course, however, is to use a conventional type of autopilot.

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### An analysis of once-per-revolution oscillating aerodynamic thrust loads on single-rotation propellers on tractor airplanes at zero yaw

**Date:**January 1, 1956

**Creator:**Rogallo, Vernon L; Yaggy, Paul F & Mccloud, John L , III

**Description:**A simplified procedure is shown for calculating the once-per-revolution oscillating aerodynamic thrust loads on propellers of tractor airplanes at zero yaw. The only flow field information required for the application of the procedure is a knowledge of the upflow angles at the horizontal center line of the propeller disk. Methods are presented whereby these angles may be computed without recourse to experimental survey of the flow field. The loads computed by the simplified procedure are compared with those computed by a more rigorous method and the procedure is applied to several airplane configurations which are believed typical of current designs. The results are generally satisfactory.

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### Analysis of plane-plastic stress problems with axial symmetry in strain-hardening range

**Date:**January 1, 1951

**Creator:**Wu, M H Lee

**Description:**A simple method is developed for solving plane-plastic-stress problems with axial symmetry in the strain-hardening range which is based on the deformation theory of plasticity employing the finite-strain concept. The equations defining the problems are first reduced to two simultaneous nonlinear differential equations involving two dependent variables: (a) the octahedral shear strain, and (b) a parameter indicating the ratio of principal stresses. By multiplying the load and dividing the radius by an arbitrary constant, it is possible to solve these problems without iteration for any value of the modified load. The constant is determined by the boundary condition. This method is applied to a circular membrane under pressure, a rotating disk without and with a central hole, and an infinite plate with a circular hole. Two materials, inconel x and 16-25-6, the octahedral shear stress-strain relations of which do not follow the power law, are used. Distributions of octahedral shear strain, as well as of principal stresses and strains, are obtained. These results are compared with the results of the same problems in the elastic range.

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### An analysis of pressure studies and experimental and theoretical downwash and sidewash behind five pointed-tip wings at supersonic speeds

**Date:**January 1, 1958

**Creator:**Boatright, William B

**Description:**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.

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### Analysis of spanwise temperature distribution in three types of air-cooled turbine blade

**Date:**January 1, 1950

**Creator:**Livingood, John N B & Brown, W Byron

**Description:**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.

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### Analysis of temperature distribution in liquid-cooled turbine blades

**Date:**October 27, 1950

**Creator:**Livingood, John N B & Brown, W Byron

**Description:**The temperature distribution in liquid-cooled turbine blades determines the amount of cooling required to reduce the blade temperature to permissible values at specified locations. This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. By means of numerical examples, comparisons are made between simplified and more complete solutions and the effects of several variables are examined. Nondimensional charts to simplify some temperature-distribution calculations are also given.

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### An analysis of the effects of aeroelasticity on static longitudinal stability and control of a swept-wing airplane

**Date:**1957?~

**Creator:**Skoog, Richard B

**Description:**A theoretical analysis has been made of the effects of aeroelasticity on the static longitudinal stability and elevator angle required for balance of an airplane. The analysis is based on the familiar stability equation expressing the contribution of wing and tail to longitudinal stability. Effects of wing, tail, and fuselage flexibility are considered. Calculated effects are shown for a swept-wing bomber of relatively high flexibility.

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### Analysis of the effects of boundary-layer control in the take-off and power-off landing performance characteristics of a liaison type of airplane

**Date:**1951

**Creator:**Horton, Elmer A; Loftin, Laurence K; Racisz, Stanley F & Quinn, John

**Description:**A performance analysis has been made to determine whether boundary-layer control by suction might reduce the minimum take-off and landing distances of a four-place or five-place airplane or a liaison type of airplane below those obtainable with conventional high-lift devices. The airplane was assumed to have a cruise duration of 5 hours at 60-percent power and to be operating from airstrips having a ground friction coefficient of 0.2 or a combined ground and braking coefficient of 0.4. The payload was fixed at 1500 pounds, the wing span was varied from 25 to 100 feet, the aspect ratio was varied from 5 to 15, and the power was varied from 300 to 1300 horsepower. Maximum lift coefficients of 5.0 and 2.8 were assumed for the airplanes with and without boundary-layer-control --equipment weight was included. The effects of the boundary-layer control on total take-off distance, total power-off landing distance, landing and take-off ground run, stalling speed, sinking speed, and gliding speed were determined.

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### Analysis of the effects of wing interference on the tail contributions to the rolling derivatives

**Date:**January 24, 1951

**Creator:**Michael, William H , Jr

**Description:**An analysis of the effects of wing interference on the tail contributions to the rolling stability derivatives of complete airplane configurations is made by calculating the angularity of the air stream at the vertical tail due to rolling and determining the resulting forces and moments. Some of the important factors which affect the resultant angularity on the vertical tail are wing aspect ratio and sweepback, vertical-tail span, and considerations associated with angle of attack and airplane geometry. Some calculated sidewash results for a limited range of plan forms and vertical-tail sizes are presented. Equations taking into account the sidewash results are given for determining the tail contributions to the rolling derivatives. Comparisons of estimated and experimental results indicate that a consideration of wing interference effects improves the estimated values of the tail contributions to the rolling derivatives and that fair agreement with available experimental data is obtained.

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### An analysis of the stability and ultimate compressive strength of short sheet-stringer panels with special reference to the influence of the riveted connection between sheet and stringer

**Date:**1956

**Creator:**Semonian, Joseph W & Peterson, James P

**Description:**A method of strength analysis of short sheet-stringer panels subjected to compression is presented which takes into account the effect that the riveted attachments between the plate and the stiffeners have on the strength of panels. An analysis of experimental data shows that panel strength is highly influenced by rivet pitch, diameter, and location and that the degree of influence for a given riveting depends on the panel configuration and panel material.

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### Analysis of thrust augmentation of turbojet engines by water injection at compressor inlet including charts for calculating compression processes with water injection

**Date:**1951?~

**Creator:**Wilcox, E Clinton & Trout, Arthur M

**Description:**A psychrometric chart having total pressure (sum of partial pressures of air and water vapor) as a variable, a Mollier diagram for air saturated with water vapor, and charts showing the thermodynamic properties of various air-water vapor and exhaust gas-water vapor mixtures are presented as aids in calculating the thrust augmentation of a turbojet engine resulting from the injection of water at the compressor inlet. Curves are presented that show the theoretical performance of the augmentation method for various amounts of water injected and the effects of varying flight Mach number, altitude, ambient-air temperature, ambient relative humidity, compressor pressure ratio, and inlet-diffuser efficiency. Numerical examples, illustrating the use of the psychrometric chart and the Mollier diagram in calculating both compressor-inlet and compressor-outlet conditions when water is injected at the compressor inlet, are presented.

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### Analysis of turbulent free-convection boundary layer on flat plate

**Date:**1951

**Creator:**Eckert, E R G & Jackson, Thomas W

**Description:**With the use of Karman's integrated momentum equation for the boundary layer and data on the wall-shearing stress and heat transfer in forced-convection flow, a calculation was carried out for the flow and heat transfer in the turbulent free-convection boundary layer on a vertical flat plate. The calculation is for a fluid with a Prandtl number that is close to 1. A formula was derived for the heat-transfer coefficient that was in good agreement with experimental data in the range of Grashof numbers from 10sup10 to 10sup12. Because of the good agreement between the theoretical formula and the experimental data, the formula may be used to obtain data for high Grashof numbers. The calculation also yielded formulas for the maximum velocity in the boundary layer and for boundary-layer thickness.

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### Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers

**Date:**February 17, 1954

**Creator:**Deissler, Robert G

**Description:**The expression for eddy diffusivity from a previous analysis was modified in order to account for the effect of kinematic viscosity on the turbulence in the region close to a wall. By using the modified expression, good agreement was obtained between predicted and experimental results for heat and mass transfer at Prandtl and Schmidt numbers between 0.5 and 3000. The effects of length-to-diameter ratio and of variable viscosity were also investigated for a wide range of Prandtl numbers.

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