bluuebunny/crossref_metadata_2025 huggingface dataset:
Linear dynamics and recurrence properties defined via essential idempotents of
Authors: PUIG DE DIOS YUNIED
Published: July 2016

Consider $\mathscr{F}$, a non-empty set of subsets of $\mathbb{N}$. An operator $T$ on $X$ satisfies property ${\mathcal{P}}_{\mathscr{F}}$ if, for any non-empty open set $U$ in $X$, there exists $x\in X$ such that $\{n\geq 0:T^{n}x\in U\}\in \mathscr{F}$. Let $\overline{{\mathcal{B}}{\mathcal{D}}}$ be the collection of sets in $\mathbb{N}$ with positive upper Banach density. Our main result is a characterization of a sequence of operators satisfying property ${\mathcal{P}}_{\overline{{\mathcal{B}}{\mathcal{D}}}}$, for which we have used a deep result of Bergelson and McCutcheon in the vein of Szemerédi’s theorem. It turns out that operators having property ${\mathcal{P}}_{\overline{{\mathcal{B}}{\mathcal{D}}}}$ satisfy a kind of recurrence described in terms of essential idempotents of $\unicode[STIX]{x1D6FD}\mathbb{N}$. We will also discuss the case of weighted backward shifts. Finally, we obtain a characterization of reiteratively hypercyclic operators.
Laser performance of the SG-III laser facility
Authors: Zheng Wanguo , Wei Xiaofeng , Zhu Qihua , Jing Feng , Hu Dongxia , Su Jingqin , Zheng Kuixing , Yuan Xiaodong , Zhou Hai , Dai Wanjun , Zhou Wei , Wang Fang , Xu Dangpeng , Xie Xudong , Feng Bin , Peng Zhitao , Guo Liangfu , Chen Yuanbin , Zhang Xiongjun , Liu Lanqin , Lin Donghui , Dang Zhao , Xiang Yong , Deng Xuewei
Published: July 2016

SG-III laser facility is now the largest laser driver for inertial confinement fusion research in China. The whole laser facility can deliver 180 kJ energy and 60 TW power ultraviolet laser onto target, with power balance better than 10%. We review the laser system and introduce the SG-III laser performance here.
A predictive quasi-steady model of aerodynamic loads on flapping wings
Authors: Wang Q. , Goosen J. F. L. , van Keulen F.
Published: July 2016

Quasi-steady aerodynamic models play an important role in evaluating aerodynamic performance and conducting design and optimization of flapping wings. The kinematics of flapping wings is generally a resultant motion of wing translation (yaw) and rotation (pitch and roll). Most quasi-steady models are aimed at predicting the lift and thrust generation of flapping wings with prescribed kinematics. Nevertheless, it is insufficient to limit flapping wings to prescribed kinematics only since passive pitching motion is widely observed in natural flapping flights and preferred for the wing design of flapping wing micro air vehicles (FWMAVs). In addition to the aerodynamic forces, an accurate estimation of the aerodynamic torque about the pitching axis is required to study the passive pitching motion of flapping flights. The unsteadiness arising from the wing’s rotation complicates the estimation of the centre of pressure (CP) and the aerodynamic torque within the context of quasi-steady analysis. Although there are a few attempts in literature to model the torque analytically, the involved problems are still not completely solved. In this work, we present an analytical quasi-steady model by including four aerodynamic loading terms. The loads result from the wings translation, rotation, their coupling as well as the added-mass effect. The necessity of including all the four terms in a quasi-steady model in order to predict both the aerodynamic force and torque is demonstrated. Validations indicate a good accuracy of predicting the CP, the aerodynamic loads and the passive pitching motion for various Reynolds numbers. Moreover, compared to the existing quasi-steady models, the presented model does not rely on any empirical parameters and thus is more predictive, which enables application to the shape and kinematics optimization of flapping wings.
Teaching a Student With Autism Spectrum Disorder On-Topic Conversational Responses With an iPad: A Pilot Study
Authors: Sng Cheong Ying , Carter Mark , Stephenson Jennifer
Published: July 2016

Scripts in written or auditory form have been used to teach conversational skills to individuals with autism spectrum disorder (ASD), but with the proliferation of handheld tablet devices the scope to combine these 2 formats has broadened. The aim of this pilot study was to investigate if a script-based intervention, presented on an iPad conversational app, would be effective in teaching basic conversation skills within a school setting. A multiple baseline with probe design across scripts was employed to teach a student with ASD on-topic responses. Experimental control was demonstrated across 2 of the 3 baselines. Surprisingly, a substantial degree of generalisation was evident, which may have compromised demonstration of experimental control. This app may be a practical and effective tool for teaching on-topic responses to an individual with ASD, and further research is warranted.
Ionospheric Modelling using GPS to Calibrate the MWA. II: Regional Ionospheric Modelling using GPS and GLONASS to Estimate Ionospheric Gradients
Authors: Arora B. S. , Morgan J. , Ord S. M. , Tingay S. J. , Bell M. , Callingham J. R. , Dwarakanath K. S. , For B.-Q. , Hancock P. , Hindson L. , Hurley-Walker N. , Johnston-Hollitt M. , Kapińska A. D. , Lenc E. , McKinley B. , Offringa A. R. , Procopio P. , Staveley-Smith L. , Wayth R. B. , Wu C. , Zheng Q.
Published: July 2016

We estimate spatial gradients in the ionosphere using the Global Positioning System and GLONASS (Russian global navigation system) observations, utilising data from multiple Global Positioning System stations in the vicinity of Murchison Radio-astronomy Observatory. In previous work, the ionosphere was characterised using a single-station to model the ionosphere as a single layer of fixed height and this was compared with ionospheric data derived from radio astronomy observations obtained from the Murchison Widefield Array. Having made improvements to our data quality (via cycle slip detection and repair) and incorporating data from the GLONASS system, we now present a multi-station approach. These two developments significantly improve our modelling of the ionosphere. We also explore the effects of a variable-height model. We conclude that modelling the small-scale features in the ionosphere that have been observed with the MWA will require a much denser network of Global Navigation Satellite System stations than is currently available at the Murchison Radio-astronomy Observatory.
Flutter of Systems with Many Freedoms
Authors: Duncan W. J.
Published: July 2016

Experience has shown that it is often necessary to retain many degrees of freedom in order to calculate critical nutter speeds reliably, but this entails much labour. Part I discusses the choice of a minimum set of freedoms and suggests that this should be based on the equation of energy and the use of the Lagrangian dynamical equation corresponding to any proposed additional freedom. The methods for conducting flutter calculations so as to minimise labour are treated in Part II.
Determination of Drag of Jet-Propelled Aircraft in Flight
Authors: Trevelyan G. W. , Blundell D. R.
Published: July 2016

In order to obtain full knowledge of the performance of an aircraft, one of the important quantities to be determined is the drag. The usual procedure is to measure the level speed of the aeroplane and to calculate the drag under these conditions from the engine thrust, as obtained from the engine makers’ specification. To do this, accurate thrust data are essential and in certain cases these may not be readily available.

In order to eliminate the possibility of systematic errors in the determination of engine thrust, a method has been developed whereby the drag at low Mach number can be measured directly,under such conditions that accurate knowledge of the engine performance is of minor importance. This method is satisfactory only on jetpropelled aircraft, since on conventional aircraft there are the added complications of propellers, slipstream, radiators and so on.

The method has been used to determine the drag of the de Havilland D.H. 100 Vampire and has given good results. The drag determined from earlier tests by the usual procedure is found to be in good agreement with that given by the new method.
Displacements of a Linear Elastic System Under a Given Transient Load
Authors: Williams D.
Published: July 2016

A method is described for obtaining the displacements (and hence the stresses) of a linear elastic system under a given transient load in a more accurate and more expeditious manner than is possible by the standard method. For simplicity, ho account is taken of damping forces in describing the method.

The method is of interest to engineers and others who require to obtain numerical answers to problems of the type described above. It depends upon the fact that in many practical cases of transient loads the inertia forces in the series of normal modes of an elastic system converge rapidly, compared with the series of “normal” loadings in terms of which the spatial distribution of the applied load can be expressed.
A Simplified Theory of “Simple Waves“
Authors: Ghaffari A.
Published: July 2016

This note is concerned with a general and exact solution of the two-dimensional equations of motion of a compressible fluid, which is steady, irrotational and isen-. tropic. The solution arrived at is the generalisation of the Prandtl-Meyer celebrated “wedge solution” to include an expansion around any smooth (or abrupt) convex boundary.

We shall obtain the solution of equations for the most general type of motion in which the Cartesian components of velocity are connected by some functional relation throughout the field of flow.

Taking into account the conditions of continuity, zero rotation and Bernoulli's equation, together with the fundamental assumption, which implies that the components of fluid velocity are each a function of fluid speed only, it is found that the motion is necessarily supersonic.

It is shown that the lines of equal speed, pressure (isobars) and density are all straight lines, although they are not necessarily concurrent as in the original Prandtl-Meyer theory, and further that the component of fluid velocity perpendicular to the isobar is equal to the local velocity of sound.

The extended Prandtl-Meyer solution for the flow past an arbitrary fixed boundary is obtained analytically.
Strength of Aeroplanes in Relation to Repeated Loads
Authors: Williams D.
Published: July 2016

The present position relating to the effect of repeated loads on aircraft structures is reviewed from the point of view of the capacity of aircraft structures to withstand such loads and also of their frequencies of occurrence in the life of the aircraft.

A rough account is given of the statistical methods by which such frequencies can be estimated, and the conclusions to which the use of these methods leads are discussed.

The note ends with an outline of a suggested programme of research and a brief statement of the conclusions reached.
Beams on elastic supports and on cross-girders
Authors: Klitchieff J. M.
Published: July 2016

The 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

The 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

Summmary

As 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

The 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

Wild 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).)
Photoelasticity and Aircraft Design
Authors: Jessop H.T. , Snell C.
Published: July 2016

It is now more than 25 years since Coker and Filon first developed photoelasticity as a practicable method of exploring the stress distribution in certain types of engineering components. All engineers must be familiar with the striking photographs of fringe patterns obtained by their method in stressed plates of various shapes viewed in a polariscope. In those early days observations were made on Xylonite models and the method was only applicable to components in which stress distribution was of a two-dimensional type. Moreover, with the apparatus then available investigations were somewhat difficult and many engineers at that time were very distrustful of the results obtained from what was, to them, a little understood laboratory technique.
A Note on the Design of Ducted Fans
Authors: Thwaites Bryan
Published: July 2016

The 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.
A Direct Aerodynamic Proof of the Biot-Savart Law
Authors: Lockwood Taylor J.
Published: July 2016

The expression for the induced velocity of a vortex element,in Glauert's notation (where K is the strength of the vortex, h the length of the normal, and r the distance from the field point to the element, of length ds) which is often known as the Biot-Savart law, and is of fundamental importance in aerodynamics, is frequently left unproved in textbooks. Sometimes reference is made to the electro-magnetic analogy, or to a standard treatise such as Lamb. One well-known work implies that the law is the solution of an integral equation derived from the known induced velocity of an infinite straight-line vortex, but this is misleading, since there is an infinite number of solutions, of which only one is correct. Another textbook gives a lengthy argument starting from the replacement of a line vortex by a sheet of sources and sinks, which is probably not too convincing to the average student. Lamb himself gives a long and rather involved proof based on Helmholtz and Stokes, with appeals to the Theory of Attractions, with which few are likely to be familiar. A simple and direct proof from fluid mechanics seems therefore worth while.
The Automatic Control of an Aeroplane in the Landing Approach onto an Aircraft Carrier
Authors: Helliwell J. B.
Published: July 2016

An 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

An 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

A 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

Four 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

Schlieren 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

An 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

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

The 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

The 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.
Note on the Stabilisation of Long Struts by an Elastic Medium
Authors: Goodey W. J.
Published: July 2016

This problem arose in connection with the stabilisation of the spar flanges of an aeroplane, where the spar passes through the fuselage. The fore-and-aft stabilisation of a compression flange in these circumstances may often be effected by means of intermediate supports, which are necessarily flexible, and the reliability of any calculations of buckling load is somewhat doubtful, mainly due to the difficulty of estimating the stiffness of the supports. In view of this it was decided in a recent design to consider a continuous support for the spar flange in the form of a thin horizontal web riveted to the flange and to the sides of the fuselage, and having a small member attached to its other edge.
Supersonic Flow Past Wing-Body Combinations
Authors: Chester W.
Published: July 2016

The 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

The 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

The 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

This 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

The 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.
Quasi-steady Derivatives for the Subsonic Flow past an Oscillating Aerofoil in a Porous Wind Tunnel
Authors: Drake D. G.
Published: July 2016

The compressible subsonic flow about an oscillating two-dimensional aerofoil in a wind tunnel with porous walls is considered. The porous wall is assumed to exhibit the property that the ratio of the normal velocity at the wall to the pressure drop across the wall is constant. The aerodynamic derivatives are found for quasi-steady pitching motion of the aerofoil. The dependence of the derivatives on Mach number and wall porosity is displayed graphically.
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.
The Drag of Ducted Bodies with Annular or Side Intakes in Supersonic Flow
Authors: Portnoy H.
Published: July 2016

A slender ducted body of arbitrary cross section is studied. This possesses an annular, side or “scoop” type of intake at some streamwise station. The parts of the body forward of and behind the intake are both permitted to have discontinuities of longitudinal profile slope at streamwise stations widely separated both from each other and from the intake. The external flow is taken to be entirely supersonic and it is assumed that the intake lip is sharp and that there is no “spill over” due to choking of the internal flow, which must be supersonic for a short distance inside the duct.
A Contribution to the Theory of Flow Stability in Multi-Stage Axial Compressors
Authors: Carter A. D. S.
Published: July 2016

Previous theories on the surging of axial compressors have been based on a quasi-static theory, whereas a finite rate of growth of the circulation around each blade must occur in practice. An examination of this factor is made in the paper, studying the stability with respect to small changes in speed instead of mass flow as in the normal approach. Effects of capacity are neglected. It is concluded that an instability occurs in the last stage of the compressor, even when that stage is itself unstalled, which could give rise to surge. It has been found necessary to introduce one empirical factor into the analysis but, when this is given a value compatible with other experimental and theoretical evidence, reasonably good agreement with experimental results is obtained.
The Stress Concentration Factors in Cylindrical Tubes with Transverse Circular Holes
Authors: Jessop H. T. , Snell C. , Allison I. M.
Published: July 2016

The “frozen stress” techniques of photoelasticity can give a complete knowledge of the stress, system in a solid body, but the examination of the stresses requires more time and care than in corresponding flat plate tests. In tests on tubes with transverse circular holes, sponsored by The Royal Aeronautical Society, all practicable geometrical shapes are examined and the maximum stress is measured in tension, bending and torsion. The results are comprehensive and show the inadequacy of previous results. In all cases the maximum stress occurs inside the bore of the hole. The accuracy of all the graphs of stress concentration factors is better than five per cent.
Stresses Around Reinforced Elliptical Holes, with Applications to Pressure Cabin Windows
Authors: Wittrick W. H.
Published: July 2016

An analytical solution, using complex variable methods, is given for the problem of the stress distribution due to an elliptical hole, reinforced around its boundary, in a plane sheet subjected at infinity either to an arbitrary constant stress system or to a bending type stress system. Numerical results were obtained for a wide range of parameters, including three different shapes of ellipse, and ten different amounts of reinforcement. Poisson's ratio was assumed to be 1/3.
The Estimation of Laminar Skin Friction, including the Effects of Distributed Suction
Authors: Curle N.
Published: July 2016

Stratford's analysis of the laminar boundary layer near separation uses two physical ideas. In the outer part of the boundary layer, where viscous effects are small, the development is given by the condition that the total head is constant along streamlines, apart from a second-order correction for viscosity. Near the wall, however, viscous forces must balance the pressure forces, and the profile adjusts itself accordingly. Quantitatively these ideas yield a simple formula for predicting separation, which has been found to be particularly accurate.

In this paper it is indicated how the same approach may be used to yield the full distribution of skin friction along the wall. Further, the effects of suction may be incorporated into the method. Physically, suction affects the outer part of the boundary layer in that the streamlines are drawn towards the wall when suction is applied. At the wall, the balance between viscous and pressure forces is influenced by the momentum of the fluid which is sucked away. When these effects are accounted for quantitatively, the resulting formula for the skin friction is still very simple.

Several examples are considered, and comparison is made with exact theory and with approximate results by other methods. It is indicated that the method has a useful range of validity.
Vibration of Rectangular Plates Point-Supported at the Corners
Authors: Cox Hugh L. , Boxer Jack
Published: July 2016

The fundamental frequencies of flexural vibration are determined for uniform isotropic rectangular plates that have free edges and pinpoint supports at the four corners. For the particular case of a square plate the lowest five frequencies and mode shapes have been determined. The second frequency is most unusual, since an infinite number of mode shapes exist with identical frequencies. Finite difference expressions, which simplify the treatment of the free boundaries for definite values of Poisson's ratio, are used in conjunction with extrapolation procedures to obtain the approximate solutions.
The Pressure Distribution on a Wing with a Subsonic Leading Edge in the Presence of Anti-symmetric Body Shaping
Authors: Jones J. G.
Published: July 2016

The pressure distribution on the wing of a centrally mounted wingbody combination due to anti-symmetrical body shaping (with respect to the wing plane) can be calculated in the case where the wing leading edge is supersonic by using the fact that the upper and lower halves of the flow field are independent and that each half can be treated by quasi-cylinder theory. When the leading edge is subsonic the anti-symmetric body shaping produces flow round the leading edge. This paper is concerned with wing pressure distributions including the effect of this flow round the leading edge.
Some Properties of the Admittances of Dynamical Chains
Authors: Duncan W. J.
Published: July 2016

Simple relations among the coefficients appearing in the admittances of dynamical chains are obtained by considering the initial motions which follow the application of certain impulses.
A Theoretical Approach to the Aerodynamically Significant Properties of Roughness from Insects
Authors: Coleman W. S.
Published: July 2016

In Reference 3, attention is drawn to the difficulties of measuring the streamwise extent of the roughness from insects. The present paper deals with the problem theoretically for an aerofoil in two-dimensional, incompressible flow. A tentative approach to the determination of effective excrescence height downstream of the leading-edge zone is also advanced. The application of these investigations, in conjunction with the analysis from Ref. 3 regarding the critical conditions for premature transition, leads to estimates of the amount of significant roughness which are in good agreement with flight observation.
Further Comments on High-Lift Testing in Wind Tunnels with Particular Reference to Jet-Blowing Models
Authors: Butler S. F. J. , Williams J.
Published: July 2016

This paper discusses some of the special problems of wind-tunnel testing which arise with high-lift jet-blowing models, supplementing earlier comments. Further detailed remarks are made about recent developments on tunnel-wall interference, test rigs and methods of minimising constraints from air-feeds to models, and on general test and model design techniques.
A Small-Bore Pick-Up for the Measurement of Fluctuating Pressures
Authors: Franklin R. E. , Archbold R. B.
Published: July 2016

The paper describes the development of a small-bore probe microphone, the frequency response of which is smoothed by arranging that the probe tube is terminated in its characteristic impedance.
The Reliability of Multiple Rocket Engines
Authors: Ruston Gillian
Published: July 2016

In assessing the merits of multiple versus single engines the possibility of a loss in reliability due to the use of more working parts must be considered. This paper gives a mathematical treatment of this problem and numerical examples illustrate the method.
The Behaviour of a Clamped Circular Plate in Compression
Authors: Sherbourne A. N.
Published: July 2016

A theoretical solution is presented for the problem of the clamped circular plate loaded in uniform compression. The solution employs a numerical method programmed for a digital computer. Instead of solving the classical von Kármán large deflection equations, a step-by-step integration of the elastic differential equations of equilibrium is carried out until suitable boundary conditions are attained. The method is an extension of one developed earlier to explain the behaviour of the simply-supported plate.
The Axial Decay and Radial Spread of a Supersonic Jet Exhausting into Air at Rest
Authors: Frauenberger J. H. , Forbister J. G.
Published: July 2016

The distribution of total pressure, stagnation temperature and gas velocity is determined for the subsonic region of a supersonic jet emerging from a solid propellant rocket motor into air at rest. Measurements of Pitot pressures in the supersonic flow region have shown that the flow follows the axis of an inclined nozzle within the order of accuracy of the measurements. Nozzle cone angle, and probably the expansion ratio, affect the jet distribution significantly.
A Comparison of the Characteristic Equations in the Theory of Circular Cylindrical Shells
Authors: Houghton D. S. , Johns D. J.
Published: July 2016

Characteristic equations are derived for thin circular shells, based on various approximations to the linear elastic theory of small deformations. By representing the deformation in a Fourier series in the circumferential direction, the roots of these equations are computed for a range of the significant parameters and compared.