bluuebunny/crossref_metadata_2025_split huggingface dataset:
Beams on elastic supports and on cross-girders
Authors: Klitchieff J. M. 
Published: July 2016

SummaryThe beam on elastic supports is often considered as a beam on a continuous elastic medium. This method can be applied only to a large number of equally spaced supports having equal rigidities. The method proposed by the author, giving the solution in the form of rapidly converging series, is not bound by this restriction, and when applied to the problem of beams supported by cross-girders reduces it to a system of linear equations, their number being equal to the number of cross-girders, while the existing approximate method leads to the same number of simultaneous differential equations.
The correction of wind tunnel nozzles for two-dimensional, supersonic flow
Authors: Meyer R. E. , Holt M. 
Published: July 2016

SummaryThe paper is concerned with the two-dimensional, steady, irrotational, isentropic flow of a perfect gas in a wind tunnel nozzle which is found to produce a flow in the test rhombus deviating slightly from the desired uniform flow.The minimum corrections are derived that must be applied to the liners in order to produce a uniform flow in the test rhombus. If the uncorrected nozzle produces a flow of uniform direction, measurement of the pressure on the axis, in the test rhombus, suffices to determine these corrections (Section 5). If not, further pressure measurements are required (Section 6). A simple test is indicated for checking whether the flow stream direction is uniform (Section 6).The method cannot be used to correct for deviations from a two-dimensional flow.
An analysis of the lift on straight, yawed and swept-back wings
Authors: Lockwood Taylor J. 
Published: July 2016

SummmaryAs is well known, standard lifting-line theory cannot be applied to a wing with sweepback in order to determine the amount and distribution of the lift. Various methods, all fairly laborious, are available, and while they give results which agree fairly well with experiment, they do not show in detail the source of the various differences due to sweep. It is with the object of separating the several effects involved, which can be regarded as distinct for practical purposes, that the present method has been developed. Since one of the items, finite-chord loss, is shared with the straight wing, although not included in simple lifting-line theory, it is calculated first for the straight wing. The wing is represented by its median or camber surface and is assumed nearly flat.
Airscrews at Supersonic Forward Speeds
Authors: Burns J. C. 
Published: July 2016

SummaryThe flow past an airscrew rotating with uniform angular velocity in a uniform supersonic stream is considered from the point of view of axes fixed in the airscrew, the motion relative to these axes being steady. A linearised equation and boundary conditions are found for the potential of the disturbance flow caused by airscrews which produce only small perturbations in the main stream. This equation is solved by expanding the potential in powers of the ratio, χ, of the tip speed of the airscrew to the speed of sound in the undisturbed stream. Equations and boundary conditions are found for the coefficients of each term of the series and it is seen that the term independent of χ satisfies the ordinary linearised potential equation for fixed axes. By subtracting suitable special integrals, the more complicated equations for the coefficients of the various powers of χ can be reduced to this ordinary potential equation. Hadamard's methods have been applied by Puckett, Evvard and, finally, Ward to the problem of finding the flow past a thin wing fixed in a supersonic stream and their methods are applied to find the terms of the series in our case. The first two terms are found explicitly for a particular type of windmill. Approximate expressions are then developed for the torque and the drag on such a windmill and the results applied in special cases. The best working conditions for windmills of this type are found by considering the effect on efficiency and power of varying the shape and the speed of rotation, within the limits imposed by the strength of the material of the airscrew.
Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers
Authors: Cooke J. C. 
Published: July 2016

SummaryWild has extended to three dimensions the von Kármán-Pohlhausen method for the laminar boundary layer flow over a fixed obstacle and used the method for an infinite yawed elliptic cylinder in a stream. In this paper the method is tested in two ways (which may be called full-Pohlhausen and semi-Pohlhausen) for the case of an infinite yawed cylinder when the velocity outside the boundary layer over the surface normal to the generators is of the form U=cxm. The exact solution is known in this case.A table of the skin friction, displacement thickness and momentum thickness is given for various values of β [=2m/(m + 1)], and the agreement is found to be fairly good for β>0 (accelerated flow) but not so good for β<0 (retarded flow).)
A Note on the Design of Ducted Fans
Authors: Thwaites Bryan 
Published: July 2016

SummaryThe design of ducted fans, and the estimation of their performance for conditions other than those of the design, are usually based on the equations of the so-called strip-theory. Existing methods of solution invariably employ some form of iteration which is more or less rapidly convergent according to the experience of the computer and the detail of the method.In this note, a solution is given which, although it is strictly an iteration, is explicit in the sense that in practice no iteration is necessary. It is shown how both design for a given performance and performance for a given fan can be calculated in one direct step.Conditions for maximum efficiency are considered in an Appendix. Here a suggestion of R. Baldur's is used to give a simple approximate solution of the strip-theory equations which can be developed to give conditions for maximum efficiency, for the special case of a constant pressure rise through the fan.
The Automatic Control of an Aeroplane in the Landing Approach onto an Aircraft Carrier
Authors: Helliwell J. B. 
Published: July 2016

SummaryAn investigation is made into the possibility of the completely automatic longitudinal control of an aircraft in the deck landing approach. The method presupposes the existence of a radio beam system transmitted from the carrier and a study is made of the motion of the aircraft down this beam under automatic control.The longitudinal motion alone of the aircraft and carrier is considered. The motion of the carrier is assumed to consist of a steady forward velocity modified by a non-pitching sinusoidal oscillation in the vertical plane.The most successful method of approach control proposed is based on the use of a single beam emanating from a source at a fixed distance above the carrier deck and fixed in direction. The preliminary pilot-controlled approach is assumed to be down the mean position of the beam, and the auto-control requires, over and above certain ideal variations of elevator angle and thrust, additional types of control of the following forms. On the elevator, displacement pitch and displacement track error control; and on the thrust, displacement track error control.Information is also forthcoming regarding the unsuitability of certain other types of control which at first sight seem promising.
The Initiation and Propagation of Fatigue Cracks in Mild Steel Pieces of Square Section
Authors: Cox H. L. , Field J. E. 
Published: July 2016

SummaryAn investigation has been made to determine the positions and directions of initiation and the directions of propagation of fatigue cracks and to examine the correlation between these positions and directions and the planes on which maximum tensile and maximum shear stresses are generated.To afford as wide a range as possible of the ratio of maximum shear stress to maximum tensile stress, tests have been made under combinations of alternating bending and torsion; and in order to separate partially the regions of high shear stress from those of high direct stress, the tests have been made on pieces of square section with the plane of bending parallel to one diagonal of the section. Two series of tests have been made; one a preliminary series on pieces having no parallel portion and the other on pieces having a parallel portion about three times the length of the side of the square section. The positions and directions of initiation and the directions of propagation of fatigue cracks have been observed and compared with the positions and directions of the maximum tensile and shear stresses.Fatigue cracks may be initiated as a result of either high shear stress or high tensile stress and in the present series of tests on mild steel, cracking in tension has occurred in preference to cracking in shear when the ratio of the tensile stress range to the shear stress range has exceeded about 1.6; for values of this ratio less than 1.6, the cracks started in shear (and vice versa); propagation along the plane of maximum shear appears to be preferred up to a slightly greater value of the tensile/shear ratio (about 1.7 possibly). The general direction of a crack formed as a result of high tension usually follows the plane of maximum tension and that of a crack formed as a result of shear usually follows the plane of maximum shear. In detail both types of crack—in this mild steel—deviate quite widely from their general directions but this deviation bears no obvious relation to the microstructure of the material. Cracks propagating along one plane of maximum shear occasionally show a marked tendency to branch along the associated plane of maximum shear; but this tendency is not always observed and in other cases no tendency to branch has been noted.
On the Conditions under which Energy can be Extracted from an Air Stream by an Oscillating Aerofoil
Authors: Lambourne N. C. 
Published: July 2016

SummaryA simple system is considered in which a two-dimensional aerofoil in an air stream performs a coupled oscillation in pitching and vertical translation. An expression for the energy transferred from stream to aerofoil is derived as a function of the frequency parameter, amplitude ratio and phase difference, and the conditions under which positive energy can be extracted from the stream are investigated. The connection between the case of zero energy transfer, and the critical flutter state is noted.Attention is confined to the incompressible case and diagrams show the results obtained when the air loads are obtained from (i) vortex sheet theory and (ii) the classical set of constant derivatives.Vortex sheet theory leads to the conclusion that, provided that the amplitude ratio and phase difference satisfy certain conditions, energy can be extracted from the stream for all values of the frequency parameter. On the other hand, the use of a set of constant derivatives places an upper limit on the values of the frequency parameter for the extraction of energy.
Correlation Between some Stability Problems for Orthotropic and Isotropic Plates under Bi-Axial and Uni-Axial Direct Stress
Authors: Wittrick W. H. 
Published: July 2016

SummaryFour buckling problems are considered, namely: —
(a) A rectangular orthotropic plate, with all edges simply supported, subjected to compression on its ends and a known compression or tension on its sides;(b) the same as (a) but with the ends clamped and sides simply supported;(c) a rectangular orthotropic plate, with the ends simply supported and sides clamped, subjected to compression on its ends; and(d) the same as (c) but with all edges clamped.In each case it is shown that the variables involved can all be combined into such a non-dimensional form that a single curve serves to give the value of the end compression required to cause buckling. This curve is identical with the curve of buckling stress coefficient against side ratio for a corresponding isotropic plate under uni-axial compression.
On the Noise Emanating from a Two-Dimensional Jet Above the Critical Pressure
Authors: Powell Alan 
Published: July 2016

SummarySchlieren photographs of a small scale approximately two-dimensional air jet in air above the critical pressure have shown the existence of an instability displaying an anti-symmetric pattern, and the associated sound field having several distinguishing characteristics, has been photographed. An elementary theory based upon the hypothesis that the acoustic energy originates from the interaction of the stream disturbances with the shock waves of the flow, and connecting the stream disturbances with the radiated sound, is suggested. This is shown to be consistent with the physical dimensions of the phenomenon and predicts a sound field in reasonable agreement with that observed after certain simplifying assumptions have been made.
Some Aspects of Laminar Boundary Layer Separation in Compressible Flow with no Heat Transfer to the Wall
Authors: Gadd G. E. 
Published: July 2016

SummaryAn analysis has been made which suggests that, with the types of pressure distribution most usual in practice and free stream Mach numbers up to 10, no serious errors would be introduced into the calculation of the laminar separation point by the assumption that σ, the Prandtl number, and ω, the index of variation of viscosity with absolute temperature, are equal to unity. (Typical actual values of σ and ω for air are 0.72 and 0.89 respectively).
On the Resistance of Screens
Authors: Wieghardt K. E. G. 
Published: July 2016

Summary
The resistance of various screens in a tube is reduced to the drag of a single piece of wire by assuming that the average velocity in the screen itself rather than the free stream velocity is the significant factor. Almost all the available tests on screens or gauzes are brought into line with a single experimental function similar to the drag of a cylinder plotted against Reynolds number.
On the Low Aspect Ratio Oscillating Rectangular Wing in Supersonic Flow
Authors: Miles John W. 
Published: July 2016

SummaryThe Laplace transform of the lift distribution on an oscillating rectangular wing in a supersonic flow is obtained by separating the linearised equation for the velocity potential in elliptic (cylindrical) co-ordinates. The results for the case of no spanwise distortion are expanded in ascending powers of the aspect ratio in order to compare with the slender body theory, and the longitudinal stability derivatives are calculated. It is found that at either supersonic or transonic speeds single-degree-offreedom instability in pitch is impossible insofar as the fourth power of the aspect ratio is neglected.
A Generalised Approach to the Local Instability of Certain Thin-Walled Struts
Authors: Chilver A. H. 
Published: July 2016

SummaryThe problem discussed is that of the elastic local instability of a uniformly compressed thin-walled strut composed of a number of flat component plates. The strut is essentially “ open ” in cross-sectional form, while reinforcing flanges are attached to the extreme edges. An overall stability equation, based on the small deflection theory of plate bending, is derived from the conditions which must hold at the common and extreme longitudinal edges of the strut.It is shown that the critical compression stress induces a mode of buckling which involves a whole number of sinusoidal half-waves in the longitudinal direction. Furthermore, the number of half-waves is common to all component plates of the strut. The general’ stability equation—a zero determinant of high order—lends itself to expansion in terms of 4th order minors, which may again be expressed in terms of seven basic functions. A knowledge of these functions is sufficient for the solution of any problem, however complex, within the scope of the general analysis.Application of the basic functions to the solution of three different problems yields results which indicate the need for considerable care in the design of thin-walled struts with reinforcing flanges. In struts of this type a longer wavelength of buckling is possible than is commonly associated with local instability problems.
Supersonic Flow Past Wing-Body Combinations
Authors: Chester W. 
Published: July 2016

SummaryThe supersonic flow past a combination of a thin wing and a slender body of revolution is discussed by means of the linearised equation of motion. The exact equation is first established so that the linearised solution can be fed back and the order of the error terms calculated. The theory holds under quite general conditions which should be realised in practice.The wing-body combination considered consists of a wing symmetrically situated on a pointed body of revolution and satisfying the following fairly general conditions. The wing leading edge is supersonic at the root, and the body is approximately cylindrical downstream of the leading edge. The body radius is of an order larger than the wing thickness, but is small compared with the chord or span of the wing.It is found that if the wing and body are at the same incidence, and the aspect ratio of the wing is greater than 2 (M2-1)-½, where M is the main stream Mach number, the lift is equivalent to that of the complete wing when isolated. If the wing only is at incidence then the lift is equivalent to that of the part of the wing lying outside the body.The presence of the body has a more significant effect on the drag. If, for example, the body is an infinite cylinder of radiusa, and the wing is rectangular with aspect ratio greater than 2(M2-1)-½, then the drag of the wing is decreased by a factor (1-2a/b), where2bis the span of the wing.When these conditions do not hold the results are not quite so simple but are by no means complicated.
The Influence of the Exit Velocity Profile on the Noise of a Jet
Authors: Powell Alan 
Published: July 2016

SummaryThe noise levels of a jet issuing from a long pipe are compared with those of a jet having a square velocity profile at the exit. A subsonic noise reduction of between 2 and 5 decibels for various conditions is found for the case of the flow emerging with an approximately “turbulent pipe-flow” velocity profile for the same maximum jet velocity, but this is at the expense of a loss in thrust of a quarter. On comparison with a jet of smaller diameter which has an equal thrust for the same maximum jet velocity, it is found that the changes in noise level are rather smaller. For jets of equal diameters, the effects on the subsonic aerodynamic noise generated of a reduction of velocity gradient near the boundary are more than offset by the increased velocities necessary near the centre of the jet to obtain equal thrust. It is concluded that if the effect of differences in initial turbulence can be neglected the use of an auxiliary flow forming a comparatively thin sheath of slower moving fluid at the exit is not likely to result in large decreases in the subsonic noise level, and that a general reduction in jet velocity is more effective.Above the critical pressure larger reductions of up to 10 decibels are found. These are consistent with a delay of the onset of the self-maintained shock-produced noise.
Adiabatic One-Dimensional Flow of a Perfect Gas through a Rotating Tube of Uniform Cross Section
Authors: Kestin K. , Zaremba S. K. 
Published: July 2016

SummaryThe paper contains an analysis of the flow of a perfect gas with constant specific heats through a rotating channel of constant cross-sectional area, as used in certain helicopter propulsion systems and wind-driven gas turbines. The analysis is restricted to the adiabatic one-dimensional treatment, the Coriolis accelerations acting across a section being disregarded.The equations of motion and energy are deduced and, together with the equation of continuity, reduced to an ordinary non-linear differential equation of the first order, involving a dimensionless form of velocity and distance.The patterns of the integral curves of the differential equation are discussed and sketched by examining their asymptotic behaviour as well as that in the neighbourhood of singular points. It is shown that there exists a critical value of the angular velocity below which the flow remains subsonic in the pipe, if the entrance velocity is subsonic; it may, however, become sonic at the exit of the pipe. For supercritical angular velocities the flow may become sonic or supersonic in the pipe if the entrance velocity attains a given “ correct” but subsonic value. A method of examining for the possibility of shock formation is indicated.The initial conditions for the differential equation are deduced for the design and for the performance problem, two new flow functions being introduced and tabulated to facilitate practical calculations. Formulae are also deduced for the calculation of the pressure and Mach number variation from the previously calculated velocity variation along the pipe.Finally an approximate solution in closed terms is given for the case of small entrance velocities.
The Wave Drag of Wing-Quasi-Cylinder Combinations at Zero Incidence
Authors: Fraenkel L. E. 
Published: July 2016

SummaryThis paper is concerned with the drag, at zero lift, of wing-body combinations which are symmetrical about the wing plane. Only two assumptions are made: that surface slopes are sufficiently small for the application of linearised theory, and that it is sufficient to satisfy the body boundary condition on the surface of a circular cylinder.The configuration is represented entirely by singularities along the body axis, and three drag formulae are derived. The first involves the Laplace transforms of functions representing the strengths of the sources and multisources; the difficult problem of inverting these transforms is thereby avoided. The second involves these strength functions themselves, and is of the form of a series of double integrals of the famous von Kármán type. The third involves functions describing the geometry of a very hypothetical quasi-cylinder which has the same drag as the Whole configuration in question. The convergence of these formulae is established.These results are then used to make an order-of-magnitude analysis for wing-slender-body combinations: a large number of drag terms are seen to be negligible when the ratio of body radius to wing chord is small, and the dominant terms for smooth bodies are those appearing in Ward's drag formula.Finally, the geometry of the “ equivalent quasi-cylinder ” is investigated.
The Employment of Aerodynamic Forces to Obtain Maximum Range of a Rocket Missile
Authors: Lawden Derek F. 
Published: July 2016

SummaryThe programming of the thrust direction of a rocket missile, to obtain maximum range over a flat earth by the most favourable employment of the aerodynamic forces, is considered for the special case when these forces are small by comparison with the missile weight. The cases of a V.2-type missile, (a) with lift and (b) without lift, are dealt with in detail and numerical results have been computed.
Symmetrically Loaded Circular Plates under the Combined Action of Lateral and End Loading
Authors: Hicks Raymond 
Published: July 2016

Expressions are obtained for the radial and tangential bending moments in a circular plate under the combined action of (a) a lateral load concentrated on the circumference of a circle and an end tension or compression, and (b) a uniformly distributed lateral load, having a diameter less than the diameter of the plate, and an end tension or compression. For both types of loading, solutions are obtained for plates which are simply-supported and for plates with an arbitrary end rotation.In addition, the following limiting cases are considered: (i) concentrated lateral load with end tension or compression, and (ii) an infinite plate under the simultaneous action of an end tension and a lateral load concentrated on the circumference of a circle of finite diameter.