This report presents the results of wind tunnel tests conducted to determine the aerodynamic characteristics of airship models. Eight Goodyear-Zeppelin airship models were tested in the original closed-throat tunnel. After the tunnel was rebuilt with an open throat a new model was tested, and one of the Goodyear-Zeppelin models was retested. The results indicate that much may be done to determine the drag of airships from evaluations of the pressure and skin-frictional drags on models tested at large Reynolds number.
This report presents the results of wind tunnel tests of two airship models conducted to determine the drag coefficients at zero pitch, and the effect of fins and cars and of flat and streamlined protuberances located at various positions along the hull. During the investigation the stern of one model was rounded off to produce a blunter shape. The extreme range of the Reynolds number based on the over-all length of the models was from 1,300,000 to 33,000,000. At large values of the Reynolds number the streamlined protuberance affected the drag very little, and the additional drag caused by the flat protuberance was less than the calculated drag by the protuberance alone. The fins and cars together increased the bare-hull drag about 20 per cent.
Section characteristics for use in wing design are presented for the NACA 23012 airfoil with plain and split flaps of 20 percent wing chord at a value of the effective Reynolds number of about 8,000,000. The flap deflections covered a range from 60 degrees upward to 75 degrees downward for the plain flap and from neutral to 90 degrees downward for the split flap. The split flap was aerodynamically superior to the plain flap in producing high maximum lift coefficients and in having lower profile-drag coefficients at high lift coefficients.
The historical development of NACA airfoils is briefly reviewed. New data are presented that permit the rapid calculation of the approximate pressure distributions for the older NACA four-digit and five-digit airfoils by the same methods used for the NACA 6-series airfoils. The general methods used to derive the basic thickness forms for NACA 6 and 7-series airfoils together with their corresponding pressure distributions are presented. Detail data necessary for the application of the airfoils to wing design are presented in supplementary figures placed at the end of the paper. The report includes an analysis of the lift, drag, pitching-moment, and critical-speed characteristics of the airfoils, together with a discussion of the effects of surface conditions. Available data on high-lift devices are presented. Problems associated with lateral-control devices, leading-edge air intakes, and interference are briefly discussed, together with aerodynamic problems of application. (author).
A method of analysis based on slender-wing theory is developed to investigate the characteristics in roll of slender cruciform wings and wing-body combinations. The method makes use of the conformal mapping processes of classical hydrodynamics which transform the region outside a circle and the region outside an arbitrary arrangement of line segments intersecting at the origin. The method of analysis may be utilized to solve other slender cruciform wing-body problems involving arbitrarily assigned boundary conditions. (author).
An investigation of the nature of the flow field behind a rectangular wing of circular arc cross section has been conducted in the Langley 9-inch supersonic tunnel. Pitot- and static-pressure surveys covering a region of flow behind the wing have been made together with detailed pitot surveys throughout the region of the wake. In addition, the flow direction has been measured by means of a weathercocking vane. Theoretical calculations have been made to obtain the variation of both downwash and sidewash with angle of attack by using the superposition method of Lagerstrom, Graham, and Grosslight. In addition, the effect of wing thickness on the sidewash with the wing at 0 degree angle of attack has been evaluated.
Symbols and definition of various airspeed terms that have been adopted as standard by the NACA subcommittee on aircraft structural design are presented. The equations, charts, and tables required in the evaluation of true airspeed, calibrated airspeed, equivalent airspeed, impact and dynamic pressures, and Mach and Reynolds numbers have been compiled. Tables of the standard atmosphere to an altitude of 65,000 feet and a tentative extension to an altitude of 100,000 feet are given along with the basic equations and constants on which both the standard atmosphere and the tentative extension are based.
The strength of modern lightweight thin-wall structures is generally limited by the strength of the compression members. An adequate design of these members requires a knowledge of the compressive stress-strain graph of the thin-wall material. The "pack" method was developed at the National Bureau of Standards with the support of the National Advisory Committee for Aeronautics to make possible a determination of compressive stress-strain graphs for such material. In the pack test an odd number of specimens are assembled into a relatively stable pack, like a "pack of cards." Additional lateral stability is obtained from lateral supports between the external sheet faces of the pack and outside reactions. The tests seems adequate for many problems in structural research.
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. The theoretical predictions of the flow-field characteristics were qualitatively correct in all cases considered, although there were indications that the magnitudes of the downwash angles tended to be overpredicted as the tip of the swept wing was approached and that the sidewash angles ahead of the unswept wing were underpredicted. The calculated effects of compressibility indicated that significant increases in the chordwise variation of flow angles and dynamic-pressure ratios should be expected in going from low to high subsonic speeds.
A series method of determining two-dimensional vortex paths is considered and applied to the computation of vortex positions behind a slender equal-span cruciform wing at any angle of bank as a function of the distance behind the trailing edge. Calculated paths are shown for four bank angles. For a bank angle of 45 degrees comparison is made with the results of a closed expression given in NACA-TN-2605. For other bank angles water-tank experiments provide qualitative comparison. Satisfactory agreement is found for a sufficient distance downstream to include most practical missile-tail positions. The interference forces on an equal-span cruciform wing are calculated for five angles of bank (including the trivial case of zero bank) from the vortex positions found by use of the series.
A method is presented for the rapid calculation of the incremental chordwise normal-force distribution over an airfoil section due to the deflection of a plain flap or tab, a split flap, or a serially hinged flap. This report is intended as a supplement to NACA Report no. 631, wherein a method is presented for the calculation of the chordwise normal-force distribution over an airfoil without a flap or, as it may be considered, an airfoil with flap (or flaps) neutral. The method enables the determination of the form and magnitude of the incremental normal-force distribution to be made for an airfoil-flap combination for which the section characteristics have been determined. A method is included for the calculation of the flap normal-force and hinge-moment coefficients without necessitating a determination of the normal-force distribution.
In this report a theory of thin airfoils of small camber is developed which permits either the velocity distribution corresponding to a given airfoil shape, or the airfoil shape corresponding to a given velocity distribution to be calculated. The procedures to be employed in these calculations are outlined and illustrated with suitable examples.
A simplified analysis of the velocity and deceleration history of ballistic missiles entering the earth's atmosphere at high supersonic speeds is presented. The results of this motion analysis are employed to indicate means available to the designer for minimizing aerodynamic heating. The heating problem considered involves not only the total heat transferred to a missile by convection, but also the maximum average and local time rates of convective heat transfer.
This report has been prepared to provide a practical method for determining the chordwise distribution of the rate of heat transfer from the surface of a wing or body of revolution to air. The method is limited in use to the determination of heat transfer from the forward section of such bodies when the flow is laminar. A comparison of the calculated average heat-transfer coefficient for the nose section of the wing of a Lockheed 12-A airplane with that experimentally determined shows a satisfactory agreement. A sample calculation is appended.
The observed flow field about slender inclined bodies of revolution is compared with the calculated characteristics based upon potential theory. The comparison is instructive in indicating the manner in which the effects of viscosity are manifest. Based on this and other studies, a method is developed to allow for viscous effects on the force and moment characteristics of bodies. The calculated force and moment characteristics of two bodies of high fineness ratio are shown to be in good agreement, for most engineering purposes, with experiment. (author).
Theoretical tunnel-wall corrections are derived for an airfoil of finite thickness and camber in a two-dimensional-flow wind tunnel. The theory takes account of the effects of the wake of the airfoil and of the compressibility of the fluid, and is based upon the assumption that the chord of the airfoil is small in comparison with the height of the tunnel. Consideration is given to the phenomenon of choking at high speeds and its relation to the tunnel-wall corrections. The theoretical results are compared with the small amount of low-speed experimental data available and the agreement is seen to be satisfactory, even for relatively large values of the chord-height ratio.
This report was prepared for the National Advisory Committee for Aeronautics and presents the results of investigations conducted by the Forest Products Laboratory of the United States Forest Service on the manufacture, preparation, application, testing and physical properties of the different types of glues used in wood airplane parts.
A theoretical analysis of helicopter maneuver stability is made and the results are compared with experimental results for both a single and a tandem rotor helicopter. Techniques are described for measuring in flight the significant stability derivatives for use with the theory to aid in design studies of means for achieving marginal maneuver stability for a prototype helicopter.
Theoretically derived charts and equations are presented by which tail-rotor design studies of directional trim and control response at low forward speed can be conveniently made. The charts can also be used to obtain the main-rotor stability derivatives of thrust with respect to collective pitch and angle of attack at low forward speeds. The use of the charts and equations for tail-rotor design studies is illustrated. Comparisons between theoretical and experimental results are presented. The charts indicate, and flight tests confirm, that the region of vortex roughness which is familiar for the main rotor is also encountered by the tail rotor and that prolonged operation at the corresponding flight conditions would be difficult.
An investigation of the lateral-directional flying qualities of a tandem-rotor helicopter in forward flight was undertaken to determine desirable goals for helicopter lateral-directional flying qualities and possible methods of achieving these goals in the tandem-rotor helicopter. Comparison between directional stability as measured in flight and rotor-off model tests in a wind tunnel shows qualitative agreement and, hence, indicates such wind-tunnel test, despite the absence of the rotors, to be one effective method of studying means of improving the directional stability of the tandem helicopter. Flight-test measurements of turns and oscillations, in conjunction with analytical studies, suggest possible practical methods of achieving the goals of satisfactory turn and oscillatory characteristics in the tandem helicopter.
The problem of the transformation of numerical values expressed in one system of units into another set or system of units frequently arises in connection with aerodynamic problems. Report contains aerodynamic coefficients and conversion tables needed to facilitate such transformation. (author).
In order to apply profitably the mathematical methods of hydrodynamics to aeronautical problems, it is necessary to make simplifications in the physical conditions of the latter. To begin with, it is allowable in many problems, as Prandtl has so successfully shown, to treat the air as having constant density and as free of viscosity. But this is not sufficient. It is also necessary to specify certain shapes for the solid bodies whose motion through the air is discussed, shapes suggested by the actual solids - airships or airfoils - it is true, but so chosen that they lead to solvable problems. In a valuable paper presented by Dr. Max M. Munk, of the National Advisory Committee for Aeronautics, Washington, to the Delft Conference in April, 1924, these necessary simplifying assumptions are discussed in detail. It is the purpose of the present paper to present in as simple a manner as possible some of the interesting results obtained by Dr. Munk's methods.
The data from previous NACA pressure-distribution investigations of plain flaps and tabs with sealed gaps have been analyzed and are presented in this paper in a form readily applicable to the problems of control-surface design. The experimentally determined variation of aerodynamic parameters with flap chord and tab chord are given in chart form and comparisons are made with the theory. With the aid of these charts and the theoretical relationships for a thin airfoil, the aerodynamic characteristics for control surfaces of any plan form with plain flaps and tabs with sealed gaps may be determined. A discussion of the basic equations of the thin-airfoil theory and the development of a number of additional equations that will be helpful in tail design are presented in the appendixes. The procedure for applying the data is described and a sample problem of horizontal tail design is included. The data presented and the method of application set forth in this report should provide a reasonably accurate and satisfactory means of computing the aerodynamic characteristics of control surfaces.
This report presents tables and charts for use in determining the characteristics of tapered wings. Theoretical factors are given from which the following characteristics of tapered wings may be found: the span lift distribution, the induced-angle-of attack distribution, the lift-curve slope, the angle of zero lift, the induced drag, the aerodynamic-center position, and the pitching moment about the aerodynamic center.
The experimental and calculated aerodynamic characteristics of 22 tapered wings are compared, using tests made in the variable-density wind tunnel. The wings had aspect ratios from 6 to 12 and taper ratios from 1:6:1 and 5:1. The compared characteristics are the pitching moment, the aerodynamic-center position, the lift-curve slope, the maximum lift coefficient, and the curves of drag. The method of obtaining the calculated values is based on the use of wing theory and experimentally determined airfoil section data. In general, the experimental and calculated characteristics are in sufficiently good agreement that the method may be applied to many problems of airplane design.
A stability analysis is made of a long flat rectangular plate subjected to a uniform longitudinal compressive stress and supported along its longitudinal edges and along one or more longitudinal lines by elastic line supports. The elastic supports possess deflectional and rotational stiffness. Such configuration is an idealization of the compression cover skin and internal structure of a wing and tail surfaces. The results of the analysis are presented in the form of charts in which the buckling-stress coefficient is plotted against the buckle length of the plate for a wide range of support stiffnesses. The charts make possible the determination of the compressive buckling stress of plates supported by members whose stiffness may or may not be defined by elementary beam bending and twisting theory but yet whose effective restraint is amenable to evaluation. The deflectional and rotational stiffness provided by longitudinal stiffeners and full-depth webs is discussed and numerical examples are given to illustrate the application of the charts to the design of wing structures.
This report presents the results of flight measurements of longitudinal stability and control characteristics made on a swept-wing jet aircraft to determine the origin of the pitch-up encountered in maneuvering flight at transonic speeds. For this purpose measurements were made of elevator angle, tail angle of attack, and wing-fuselage pitching moments (obtained from measurements of the balancing tail loads).
The results of two investigations, one to determine the relative merits of four experimental and two conventional design 75-millimeter-bore (size 215) cylindrical roller bearings and one to determine the relative merits of nodular iron and bronze as cage materials for this size and type of bearing, are presented in this report. Nine test bearings were operated over a range of dn values (product of bearing bore in mm and shaft speed in r.p.m) from 0.3 x 10(6) to 2.3 x 20(6), radial loads for 7 to 1613 pounds, and oil flows from 2 to 8 pounds per minute with a single-jet circulatory oil feed. Of the six bearings used to evaluate designs, four were experimental types with outer-race-riding cages and inner-race-guided rollers, and two were conventional types, one with outer-race-guided rollers and cage and one with inner-race-guided rollers and cage. Each of these six test bearings was equipped with a different design cage made of nodular iron. The experimental combination of an outer-race-riding cage with a straight-through outer race and inner-race-guided rollers was found to give the best over-all performance based on limiting dn values and bearing temperatures.
An analysis of the nose-inlet shapes developed in previous investigations to represent the optimum from the standpoint of critical speed has shown that marked similarity exists between the nondimensional profiles of inlets which have widely different proportions and critical speeds. With the nondimensional similarity of such profiles established, the large differences in the critical speeds of these nose inlets must be a function of their proportions. An investigation was undertaken in the Langley 8-foot high-speed tunnel to establish the effects of nose-inlet proportions on critical Mach number to develop a rational method for the design of high-critical-speed nose inlets to meet desired requirements. The test results data have been arranged in the form of design charts from NACA 1-series nose-inlet proportions and can be selected for given values of critical Mach number and airflow quantity. Examples of nose-inlet selections are presented for a typical jet-propulsion installation (critical Mach number of 0.83) and for two conventional radial-engine installations (critical Mach number of 0.76).
This work was undertaken to obtain results on a small model of a complete airplane which might be used for comparison with corresponding tests made in full flight. Somewhat similar tests have been previously made at various other laboratories; but as certain discrepancies exist between corresponding tests in different tunnels, it has been deemed advisable to obtain a direct comparison for this particular installation. The present work covers tests on a one-twenty-fourth scale model at speeds varying from 6.7 m/sec. (15 m.p.h.) to 40.2 m/sec, (90 m.p.h.). A slip stream correction has been obtained by the use of a small belt-driven propeller mounted in front of the model, and force coefficients thus obtained are compared with the measurements of the same forces made in full flight on a geometrically similar airplane. This report gives lift, drag, and longitudinal moment values obtained in tests of a particularly accurate model over a wide range of speeds. A measure of the slip stream corrections on lift and drag forces was obtained by the use of a power-driven model propeller. Measurements were also made of forces and longitudinal moments for all angles from 0 degree to 360 degrees.
To supplement the standardization tests now in progress at several laboratories, a broad investigation of the resistance of spheres in wind tunnels and free air has been carried out by the National Advisory Committee for Aeronautics. The subject has been classed in aerodynamic research, and in consequence there is available a great mass of data from previous investigations. This material was given careful consideration in laying out the research, and explanation of practically all the disagreement between former experiments has resulted. A satisfactory confirmation of Reynolds law has been accomplished, the effect of means of support determined, the range of experiment greatly extended by work in the new variable density wind tunnel, and the effects of turbulence investigated by work in the tunnels and by towing and dropping tests in free air. It is concluded that the erratic nature of most of the previous work is due to support interference and differing turbulence conditions. While the question of support has been investigated thoroughly, a systematic and comprehensive study of the effects of scale and quality of turbulence will be necessary to complete the problem, as this phase was given only general treatment.
This investigation was carried out in the 5-foot wind tunnel of the Langley Memorial Aeronautical Laboratory for the purpose of obtaining more complete information on the distribution of lift between the ends of wing spars, the stresses in ailerons, and the general subject of airflow near the tip of a wing. It includes one series of tests on four models without ailerons, having square, elliptical, and raked tips respectively, and a second series of positively and negatively raked wings with ailerons adjusted to different settings. The results show that negatively raked tips give a more uniform distribution of air pressure than any of the other three arrangements, because the tip vortex does not disturb the flow at the trailing edge. Aileron loads are found to be less severe on wings with negative application to the calculation of aileron and wing stresses and also to facilitate the proper distribution of load in sand testing. Contour charts show in great detail the complex distribution lift over the wing.
Theoretical derived expressions for the flapping, the thrust, the torque, and the profile drag-lift ratio of nonfeathering rotor with hinged, rectangular, linearly twisted blades are given as simple functions of the inflow velocity and the blade pitch. Representative values of the coefficients of each of the terms in these expressions are tabulated for a series of specified values of the tip-speed ratio. Analysis indicates that the tabulated values can be used to calculate, with reasonable accuracy, the characteristics of any rotor of conventional design.
Two improvements have been made in the method developed in NACA Reports nos. 487 and 591 for the estimation of the inflow velocity required to overcome a given decelerating torque in an autogiro rotor. At low tip-speed ratios, where the assumptions necessary for the analytical integrations of the earlier papers are valid, the expressions therein derived are greatly simplified by combining and eliminating terms with a view of minimizing the numerical computations required. At high tip-speed ratios, by means of charts based on graphical integrations, errors inherent in the assumptions associated with the analytical method are largely eliminated. The suggested method of estimating the inflow velocity presupposes a knowledge of the decelerating torque acting on the rotor; all available full-scale experimental information on this subject is included.
Report presents the results of tests of a 1/10-scale model of the XN2Y-1 airplane tested in the NACA 5-foot vertical wind tunnel in which the six components of forces and moments were measured. The model was tested in 17 attitudes in which the full-scale airplane had been observed to spin, in order to determine the effects of scale, tunnel, and interference. In addition, a series of tests was made to cover the range of angles of attack, angles of sideslip, rates of rotation, and control setting likely to be encountered by a spinning airplane. The data were used to estimate the probable attitudes in steady spins of an airplane in flight and of a model in the free-spinning tunnel. The estimated attitudes of steady spin were compared with attitudes measured in flight and in the spinning tunnel. The results indicate that corrections for certain scale and tunnel effects are necessary to estimate full-scale spinning attitudes from model results.
A preliminary investigation of the effects of changes in the elevator and rudder settings and of small changes in attitude upon the aerodynamic forces and moments exerted upon a spinning airplane was undertaken with the spinning balance in the 5-foot vertical tunnel of the National Advisory Committee for Aeronautics. The tests were made on a 1/12-scale model of the ny-1 airplane. Data by which to fix the attitude, the radius of spin, and the rotational and air velocities were taken from recorded spins of the full-scale airplane. Two spinning conditions were investigated. All six components of the aerodynamic reaction were measured and are presented in coefficient form refereed to airplane axes. The results indicate that the change in yawing moment produced by the rudder with the elevator up was the only component of force or moment produced by the elevator and rudder that could not have been balanced in an actual spin by small changes in attitude and angular velocity.
A series of wind tunnel tests of a rectangular Clark Y wing was made with the NACA spinning balance as part of a general program of research on airplane spinning. All six components of the aerodynamic force and moment were measured throughout the range of angles of attack, angles of sideslip, and values omega b/2v likely to be attained by a spinning airplane; the results were reduced to coefficient form. It is concluded that a conventional monoplane with a rectangular Clark y wing can be made to attain spinning equilibrium throughout a wide range of angles of attack but that provision of a yawing moment coefficient of -0.02 (against the spin) by the tail, fuselage, and interferences will insure against attainment of equilibrium in a steady spin.
This report presents the results of an investigation to determine the effect of boundary layer control on the lift and drag of an airfoil. Boundary layer control was accomplished by means of a backward-opening slot in the upper surface of the hollow airfoil. Air was caused to flow through this slot by a pressure which was maintained inside the airfoil by a blower. Various slot locations, slot openings, and wing pressures were used. The tests were conducted in the 5-foot atmospheric wind tunnel of the Langley Memorial Aeronautical Laboratory. Under the test conditions, the maximum lift coefficient was increased about 96 per cent for one slot arrangement, and the minimum drag coefficient was decreased about 27 per cent for another, both being compared with the results obtained with the unslotted airfoil. It is believed from this investigation that the above effects may be increased by the use of larger slot openings, better slot locations, multiple slots, improved airfoil profiles, and trailing edge flaps.
Tests have been made at high speeds to determine the drag of models, simulating propeller shanks, in the form of a circular cylinder and three airfoils, the NACA 16-025, the NACA 16-040, and the NACA 16-040 with the rear 25 percent chord cut off. All the models had a maximum thickness of 4 1/2 inches to conform with average propeller-shank dimensions and a span of 20 1/4 inches. For the tests the models were supported perpendicular to the lower surface of the wing of an XP-51 airplane. A wake-survey rake mounted below the wing directly behind the models was used to determine profile drag of Mach numbers of 0.3 to 0.8 over a small range of angle of attack. The drag of the cylinder was also determined from pressure-distribution and force measurements.
An experimental and analytical investigation of the flutter of sweptback cantilever wings is reported. The experiments employed groups of wings swept back by rotating and by shearing. The angle of sweep range from 0 degree to 60 degrees and Mach numbers extended to approximately 0.85. A theoretical analysis of the air forces on an oscillating swept wing of high length-chord ratio is developed, and the approximations inherent in the assumptions are discussed. Comparison with experiment indicates that the analysis developed in the present report is satisfactory for giving the main effects of sweep, at least for nearly uniform cantilever wings of high and moderate length-chord ratios.
Charts are presented that permit the estimation of F-3 and F-4 knock-limited performance ratings for certain ternary and quaternary fuel blends. Ratings for various ternary and quaternary blends estimated from these charts compare favorably with experimental F-3 and F-4 ratings. Because of the unusual behavior of some of the aromatic blends in the F-3 engine, the charts for aromatic-paraffinic blends are probably less accurate than the charts for purely paraffinic blends.
This report is a compilation of many of the pertinent research data acquired by the National Advisory Committee for Aeronautics on fuel performance in piston engines. The original data for this compilation are contained in many separate NACA reports which have in the present report been assembled in logical chapters that summarize the main conclusions of the various investigations. Complete details of each investigation are not included in this summary; however, such details may be found, in the original reports cited at the end of each chapter.
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.
This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.
An exact solution and a closely concurring approximate energy solution are given for the buckling of an infinitely long flat plate under combined shear and transverse direct stress with edges elastically restrained against rotation. It was found that an appreciable fraction of the critical stress in pure shear may be applied to the plate without any reduction in the transverse compressive stress necessary to produce buckling. An interaction formula in general use was shown to be decidedly conservative for the range in which it is supposed to apply.
Empirical design curves are presented for the critical stress of thin-wall cylinders loaded in axial compression. These curves are plotted in terms of the nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75.
The principal result obtained in this report is a generalization of Taylor's formula for a simple eddy. The discussion of the properties of the eddy indicates that there is a slight analogy between the theory of eddies in a viscous fluid and the quantum theory of radiation. Another exact solution of the equations of motion of viscous fluid yields a result which reminds one of the well-known condition for instability in the case of a horizontally stratified atmosphere.
This report deals with the investigation of the apparent inertia of an airship hull. The exact solution of the aerodynamical problem has been studied for hulls of various shapes and special attention has been given to the case of an ellipsoidal hull. In order that the results for this last case 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 motion by means of a formula involving a coefficient K 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 7. For rough purposes it is sufficient to employ the coefficients, originally found for ellipsoids, for hulls otherwise shaped. When more exact values of the inertia are needed, estimates may be based on a study of the way in which K varies with different characteristics and for such a study the new coefficient possesses some advantage over one which is defined with reference to the volume of fluid displaced. The case of rotation of an airship hull has been investigated also and a coefficient has been defined with the same advantages as the corresponding coefficient for rectilinear motion.
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.
In this report a study is made of the effect on longitudinal and lateral oscillations of an airplane of simultaneous variations in two resistance derivatives while the remainder of the derivatives are constant. The results are represented by diagrams in which the two variable resistance derivatives are used as coordinates, and curves are plotted along which the modulus of decay of a long oscillation has a constant value. The same type of analysis is also carried out for the stability of the parachute. In discussing the stability of the helicopter it is concluded that the gyroscopic effect on stability will be greater than in the case of the airplane.
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