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The Theory of the Pitot and Venturi Tubes, Part 2: Report discussing several aspects of pitot and venturi tubes, including the energy equation for steady adiabatic flow, introduction of mean speed into the energy equation, isentropic flow of an ideal gas, the theory of the pitot tube, and the theory of the venturi meter.
Flow and Drag Formulas for Simple Quadrics: 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.
Flow and Force Equations for a Body Revolving in a Fluid: 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.
The Minimum Induced Drag of Aerofoils: 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 Aerodynamic Forces on Airship Hulls: 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.
Applications of Modern Hydrodynamics to Aeronautics Part 1: Fundamental Concepts and the Most Important Theorems. Part 2: Applications: 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.
Boron and zirconium from crucible refractories in a complex heat-resistant alloy: 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.
Characteristics of the Langley 8-Foot Transonic Tunnel With Slotted Test Section: "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" (p. 1297).
Measurements of free-space oscillating pressures near propellers at flight Mach numbers to 0.72: "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" (p. 999).
Area-Suction Boundary-Layer Control as Applied to the Trailing-Edge Flaps of a 35 Degree Swept-Wing Airplane: "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" (p. 1).
Blowing-type boundary-layer control as applied to the trailing-edge flaps of a 35 degree swept-wing airplane: 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.
Systematic two-dimensional cascade tests of NACA 65-series compressor blades at low speeds: The performance of NACA 65-series compressor blade section in cascade has been investigated systematically in a low-speed cascade tunnel. Porous test-section side walls and for high-pressure-rise conditions, porous flexible end walls were employed to establish conditions closely simulating two-dimensional flow. Blade sections of design lift coefficients from 0 to 2.7 were tested over the usable angle-of-attack range for various combinations of inlet-flow angle. A sufficient number of combinations were tested to permit interpolation and extrapolation of the data to all conditions within the usual range of application. The results of this investigation indicate a continuous variation of blade-section performance as the major cascade parameters, blade camber, inlet angle, and solidity were varied over the test range. Summary curves of the results have been prepared to enable compressor designers to select the proper blade camber and angle of attack when the compressor velocity diagram and desired solidity have been determined.
A Correlation of Results of Flight Investigation With Results of an Analytical Study of Effects of Wing Flexibility on Wing Strains Due to Gusts: 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.
A Low-Speed Experimental Investigation of the Effect of a Sandpaper Type of Roughness on Boundary-Layer Transition: Report describing the effects of an area of roughness on the velocity and turbulence measurements of an airfoil. It details the effects of the size, location, and height of the roughness on the Reynolds number. From Summary: "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."
NACA Research on Slurry Fuels: "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" (p. 1273).
Thin airfoil theory based on approximate solution of the transonic flow equation: A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Drag Minimization for Wings and Bodies in Supersonic Flow: "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" (p. 1213).
Effect of fuel variables on carbon formation in turbojet-engine combustors: 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.
Investigation of a nonlinear control system: 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.
Growth of Disturbances in a Flame-Generated Shear Region: 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.
Relation of Turbojet and Ramjet Combustion Efficiency to Second-Order Reaction Kinetics and Fundamental Flame Speed: Theoretical studies of the turbojet and ramjet combustion process are summarized and the resulting equations are applied to experimental data obtained from various combustor tests. The theoretical treatment assumes that one step in the over-all chain of processes which constitute jet-engine combustion is sufficiently slow to be the rate-controlling step that determines combustion efficiency.
Elliptic Cones Alone and with Wings at Supersonic Speed: "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" (p. 975).
The Mechanism of Thermal-Gradient Mass Transfer in the Sodium Hydroxide-Nickel System: "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.
A Method of Computing the Transient Temperature of Thick Walls From Arbitrary Variation of Adiabatic-Wall Temperature and Heat-Transfer Coefficient: "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" (p. 877).
Calculated and Measured Stresses in Simple Panels Subject to Intense Random Acoustic Loading Including the Near Noise Field of a Turbojet Engine: "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" (p. 703).
Approximate analysis of effects of large deflections and initial twist on torsional stiffness of a cantilever plate subjected to thermal stresses: From Summary: "An approximate analysis of the nonlinear effects of initial twist and large deflections on the torsional stiffness of a cantilever plate subjected to a nonuniform temperature distribution is presented. The Von Karman large-deflection equations are satisfied through the use of a variational principle. The results show that initial twist and applied moments can have significant effects on the changes in stiffness produced by nonuniform heating, particularly in the region of the buckling temperature difference. Results calculated by this approximate analysis are in satisfactory agreement with measured torsional deformations and changes in natural frequency."
Survey of hydrogen combustion properties: This literature digest of hydrogen-air combustion fundamentals presents data on flame temperature, burning velocity, quenching distance, flammability limits, ignition energy, flame stability, detonation, spontaneous ignition, and explosion limits. The data are assessed, recommended values are given, and relations among various combustion properties are discussed. New material presented includes: theoretical treatment of variation in spontaneous ignition lag with temperature, pressure, and composition, based on reaction kinetics of hydrogen-air composition range for 0.01 to 100 atmospheres and initial temperatures of 0 degrees to 1400 degrees k.
Compressible Laminar Boundary Layer Over a Yawed Infinite Cylinder With Heat Transfer and Arbitrary Prandtl Number: "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" (p. 1017).
On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field: 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.
A variational theorem for creep with applications to plates and columns: A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.
A phenomenological relation between stress, strain rate, and temperature for metals at elevated temperatures: Report presenting a phenomenological relation between stress, strain rate, and temperature to account for the behavior of polycrystalline metals above the equicohesive temperature. This is because the behavior of metals at elevated temperatures is constantly becoming a more important problem. The validity of the relation suggested in the equation appears to be accurate for 7075-T6 aluminum alloy.
Ground Simulator Studies of the Effects of Valve Friction, Stick Friction, Flexibility, and Backwash on Power Control System Quality: 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.
Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades: 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.
Full-Scale Investigation of Several Jet-Engine Noise-Reduction Nozzles: "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" (p. 1249).
Origin and Prevention of Crash Fires in Turbojet Aircraft: "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" (p. 623).
Attenuation in a Shock Tube Due to Unsteady-Boundary-Layer Action: "A method is presented for obtaining the attenuation of a shock wave in a shock tube due to the unsteady boundary layer along the shock-tube walls. It is assumed that the boundary layer is thin relative to the tube diameter and induces one-dimensional longitudinal pressure waves whose strength is proportional to the vertical velocity at the edge of the boundary layer. The contributions of the various regions in a shock tube to shock attenuation are indicated. The method is shown to be in reasonably good agreement with existing experimental data" (p. 1).
Basic considerations in the combustion of hydrocarbon fuels with air: Basic combustion research is collected, collated, and interpreted as it applies to flight propulsion. The following fundamental processes are treated in separate chapters: atomization and evaporation of liquid fuels, flow and mixing processes in combustion chambers, ignition and flammability of hydrocarbon fuels, laminar flame propagation, turbulent flames, flame stabilization, diffusion flames, oscillations in combustors, and smoke and coke formation in the combustion of hydrocarbon-air mixtures. Theoretical background, basic experimental data, and practical significance to flight propulsion are presented.
Determination of longitudinal stability and control characteristics from free-flight model tests with results at transonic speeds for three airplane configurations: From Summary: "A test technique and data analysis method has been developed for determining the longitudinal aerodynamic characteristics from free-flight tests of rocket-propelled models. The technique makes use of accelerometers and an angle-of-attack indicator to permit instantaneous measurements of lift, drag, and pitching moments. The data, obtained during transient oscillations resulting from control-surface disturbances, are analyzed by essentially nonlinear direct methods (such as cross plots of the variation of lift coefficient with angle of attack) and by linear indirect methods by using the equations of motion for a transient oscillation."
Experimental and predicted longitudinal and lateral-directional response characteristics of a large flexible 35 degree swept-wing airplane at an altitude of 35,000 feet: Measured and predicted dynamic response characteristics of a large flexible swept-wing airplane to control surface inputs are presented for flight conditions of 0.6 to 0.85 Mach number at an altitude of 35,000 feet. The report is divided into two parts. The first part deals with the response of the airplane to elevator control inputs with principal responses contained in a band of frequencies including the longitudinal short-period mode and several symmetrical structural modes. The second part deals with the response of the airplane to aileron and rudder control inputs with principal responses contained in a band of frequencies including the dutch roll mode, the rolling mode, and three antisymmetrical structural modes.
Far Noise Field of Air Jets and Jet Engines: "An experimental investigation was conducted to study and compare the acoustic radiation of air jets and jet engines. A number of different nozzle-exit shapes were studied with air jets to determine the effect of exit shape on noise generation. Circular, square, rectangular, and elliptical convergent nozzles and convergent-divergent and plug nozzles were investigated" (p. 1).
Flight and analytical methods for determining the coupled vibration response of tandem helicopters: Chapter one presents a discussion of flight-test and analysis methods for some selected helicopter vibration studies. The use of a mechanical shaker in flight to determine the structural response is reported. A method for the analytical determination of the natural coupled frequencies and mode shapes of vibrations in the vertical plane of tandem helicopters is presented in Chapter two. The coupled mode shapes and frequencies are then used to calculate the response of the helicopter to applied oscillating forces.
An investigation of single- and dual-rotation propellers at positive and negative thrust, and in combination with an NACA 1-series D-type cowling at Mach numbers up to 0.84: From Summary: "An investigation has been made to determine the aerodynamic characteristics of the NACA 4-(5)(05)-041 four-blade, single-relation propeller and the NACA 4-(5)(05)-037 six- and eight-blade, dual-rotation propellers in combination with various spinners and NACA d-type spinner-cowling combinations at Mach numbers up to 0.84. Propeller force characteristics, local velocity distributions in the propeller planes, inlet pressure recoveries, and static-pressure distributions on the cowling surfaces were measured for a wide range of blade angles, advance ratios, and inlet-velocity ratios. Included are data showing: (a) the effect of extended cylindrical spinners on the characteristics of the single-rotation propeller, (b) the effect of variation of the difference in blade angle setting between the front and rear components of the dual-rotation propellers, (c) the negative- and static-thrust characteristics of the propellers with 1 series spinners, and (d) the effects of ideal- and platform-type propeller-spinner junctures on the pressure-recovery characteristics of the single-rotation propeller-spinner-cowling combination."
Near Noise Field of a Jet-Engine Exhaust: From Summary: "Aircraft structures located in the near noise field of a jet engine are subjected to extremely high fluctuating pressures that may cause structural fatigue. Studies of such structures have been limited by lack of knowledge of the loadings involved. The acoustic near field produced by the exhaust of a stationary turbojet engine having a high pressure ratio was measured for a single operating condition without burning. The maximum overall sound pressure without afterburning was found to be about 42 pounds per square foot along the jet boundary in the region immediately downstream of the jet-nozzle exit."
Seat Design for Crash Worthiness: "A study of many crash deceleration records suggested a simplified model of a crash deceleration pulse, which incorporates the essential properties of the pulse. The model pulse is considered to be composed of a base pulse on which are superimposed one or more secondary pulses of shorter duration. The results of a mathematical analysis of the seat-passenger deceleration in response to the airplane deceleration pulse are provided. On the basis of this information, presented as working charts, the maximum deceleration loads experienced by the seat and passenger in response to the airplane deceleration pulse can be computed" (p. 1).
A Second-Order Shock-Expansion Method Applicable to Bodies of Revolution Near Zero Lift: "A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2" (p. 1).
Theoretical and Experimental Investigation of the Subsonic-Flow Fields Beneath Swept and Unswept Wings with Tables or Vortex-Induced Velocities: "The flow-field characteristics beneath swept and unswept wings as determined by potential-flow theory are compared with the experimentally determined flow fields beneath swept and unswept wing-fuselage combinations. The potential-flow theory utilized considered both spanwise and chordwise distributions of vorticity as well as the wing-thickness effects. The perturbation velocities induced by a unit horseshoe vortex are included in tabular form" (p. 1).
Measurement of Static Pressure on Aircraft: "Existing data on the errors involved in the measurement of static pressure by means of static-pressure tubes and fuselage vents are presented. The errors associated with the various design features of static-pressure tubes are discussed for the condition of zero angle of attack and for the case where the tube is inclined to flow. Errors which result from variations in the configuration of static-pressure vents are also presented" (p. 645).
Methods for obtaining desired helicopter stability characteristics and procedures for stability predictions: 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.
Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition: 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.
A theoretical and experimental study of planing surfaces including effects of cross section and plan form: A summary is given of the background and present status of the pure-planing theory for rectangular flat plates and v-bottom surfaces. The equations reviewed are compared with experiment. In order to extend the range of available planing data, the principal planing characteristics for models having sharp bottom surfaces having constant angles of dead rise of 20 degrees and 40 degrees. Planing data were also obtained for flat-plate surfaces with very slightly rounded chines for which decreased lift and drag coefficients are obtained.

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