bluuebunny/crossref_metadata_2025 huggingface dataset:
A Study of the Various Boundary Conditions for Electrical Analogue Solutions of the Extension and Flexure of Flat Plates
Authors: Redshaw S. C. , Rushton K. R.
Published: July 2016

The application of electrical analogue methods to the analysis of the extension and flexure of flat plates is reviewed and the difficulties encountered in the satisfaction of the various boundary conditions are discussed. A new method for treating certain boundary conditions and the operation of the electrical analogue is described. New experimental results for two cases which present great analytical difficulty, the flexure of a plate with a free edge and a plate supported on columns, are given.
The Effects of Heat Transfer on Laminar-Boundary-Layer Separation in Supersonic Flow
Authors: Curle N.
Published: July 2016

By generalising earlier work, an approximate method is derived for calculating compressible laminar boundary layers with an unfavourable pressure gradient, with the wall temperature and Prandtl number arbitrary and some allowance made for the viscosity-temperature law. The method merely requires two quadratures and uses tables of universal functions. On the basis of this method it is suggested that when the wall is at uniform temperature the viscosity-temperature law should make little difference to the results, and that, when the wall temperature varies spatially by a factor of two, the use of a linear relationship may introduce errors of order 4 per cent in the momentum thickness. It is further suggested that the effects of Prandtl number differing from unity will increase as either the Mach number is increased or the wall is cooled. These general conclusions are borne out by detailed numerical calculations in a few selected cases.
The Influence of the Coefficient of Friction on the Elastic Stress Concentration Factor for a Pin-Jointed Connection
Authors: Lambert T. H. , Brailey R. J.
Published: July 2016

The benefit to be obtained by using an interference fit between the pin and plate in a pin-jointed connection has already been established. An examination of the published results shows that some non-linearity occurs in the mechanism of load transference from the pin to the plate since, except at very high initial interference, doubling the load on the joint more than doubles the maximum shear stress in the plate. An examination of the stress-load relationship shows a distinct discontinuity, the load at which this discontinuity occurs being dependent upon both the initial interference and the coefficient of friction between the pin and the plate. It is shown that the results hitherto published correspond to a coefficient of friction between the pin and the plate of 0.3 and results for lower and higher coefficients are given.
The Deformational Behaviour of Low Aspect Ratio Multi-Web Wings
Authors: Gallagher R. H. , Rattinger I.
Published: July 2016

Results of a study of the accuracy attainable from various approaches to low aspect ratio wing deformational analyses are described. Seven model multi-web wings, representing a restricted range of sweep angles, aspect ratios and other geometric factors, were tested for deflection influence coefficients; Part I gave experimental data. This paper describes, applies, and compares certain elementary and plate bending theories. A subsequent paper will deal with discrete element idealisations commonly employed in matrix structural analysis.
Characteristic Equations in the Theory of Circular Cylindrical Shells
Authors: Holand Ivar
Published: July 2016

Closed form solutions are given of the characteristic equation of the Hiigge theory with circumferential series expansion. Specialisations to simplified theories are shown.
The Elastic Stress Concentration Factors in Shouldered Shafts
Authors: Allison I. M.
Published: July 2016

The description of a photoelastic investigation, initiated by the Structures Committee of the Royal Aeronautical Society, into the elastic stress concentration factors associated with shouldered shafts subjected to various simple forms of loading is completed in this part of the paper. A general description of the manufacture of the models, the photoelastic techniques employed to evaluate the s.c.f. and the results of the tests on shouldered shafts subjected to torsion and to bending have been given in the previous two parts.

The present paper includes the results of the tests on shafts subjected to axial load, together with details of a supplementary investigation into the limiting value of the s.c.f., for a particular shoulder radius, as the depth of the shoulder is increased to infinity. A summary of the general conclusions for all forms of loading is given at the end of the paper.
The Deformational Behaviour of Low Aspect Ratio Multi-Web Wings
Authors: Gallagher R. H. , Rattingerj I.
Published: July 2016

Results of a study of the accuracy attainable from various approaches to low aspect ratio wing deformational analysis are described. Seven model multi-web wings, representing a restricted range of sweep angles, aspect ratios and other geometric factors, were tested for deflection influence coefficients and various analytical approaches were applied in the prediction of these results. Part I gave the experimental data; Part II dealt with analyses based on elementary and plate bending theories. This part describes and applies certain discrete element idealisations common to matrix structural analysis. The merits and shortcomings of the theories studied herein are reviewed and other promising approaches are discussed.
Decay of a Viscous Trailing Vortex
Authors: Dosanjh D. S. , Gasparek E. P. , Eskinazi S.
Published: July 2016

An experimental investigation of the viscous decay of a steady, three-dimensional, helical vortex is presented. The vortex was generated by a rectangular, symmetrical half aerofoil (N.A.C.A. 0009) of 10·5 in. span, 3 in. chord, cantilevered from the wall of the circular test section of a low speed wind tunnel. Only the local total head and flow directions were measured with a five-hole pressure sensitive probe at one to eight chord lengths behind the trailing edge of the aerofoil, and the radial, tangential and axial velocity distributions in the trailing vortex were derived. The static pressure variation in the vortex flow and the difficulties in its accurate measurement are discussed. All tests were performed at a Reynolds number based on the free-stream velocity and chord length of the aerofoil of 10,000.

The various experimental velocity distributions in the vortex were in good agreement with a linearised, axi-symmetric, laminar, incompressible, viscous vortex due to Newman. The decay of velocity and geometry parameters, however, were found to be approximately eight to ten times faster than predicted by the analysis based on a laminar kinematic viscosity. It was also observed that the amount of circulation which actually rolled up in the trailing vortex was only about 58 per cent of that expected around the (N.A.C.A. 0009) aerofoil used for this investigation.
Heat Transfer Through a Compressible Laminar Boundary Layer
Authors: Curle N.
Published: July 2016

A simple method is presented for calculating the heat transfer rate through a compressible laminar boundary layer. The temperature of the wall is assumed to be uniform, the viscosity being proportional to the absolute temperature with a ratio which may vary in an appropriate manner with position along the wall; the Prandtl number is arbitrary but greater than about 0·5.

The method assumes, following Lighthill, that heat transfer rates are determined mainly by the form of the velocity field in regions close to the wall. After applying the Ulingworth-Stewartson transformation the velocity is expanded in powers of the distance Y normal to the wall, three terms being retained. The first term, proportional to the skin friction, is zero near to a position of boundary layer separation. The second term is proportional to the pressure gradient and also to the wall temperature. Accordingly it can become close to zero when the wall is sufficiently cooled. The third term becomes important only when the first two are simultaneously close to zero and is proportional to the heat transfer rate. Since the three terms cannot, in fact, ever be all zero at the same position they form a uniformly valid non-trivial approximation to the velocity close to the wall.

With this velocity profile, and following similarity arguments first given by Liepmann, it is possible to reduce the integrated thermal energy equation to a first-order ordinary differential equation for the heat transfer rate, which is easily solved.

A comparison with an accurate solution of Poots, for a particular pressure gradient and wall temperature, yields agreement to within 1 per cent at one third of the distance from leading edge to separation and 3 per cent at twice this distance, with the error rising to 16 per cent at separation where the heat transfer rate is, of course, very low. The modesty of this error is very encouraging.
Approximate Methods of Solving the Laminar Boundary-Layer Equations
Authors: Terrill R. M.
Published: July 2016

Curie and Skan have modified the approximate methods of Thwaites and Stratford to predict separation properties of laminar boundary layers for flow over an impermeable surface. The work of Curie and Skan has been extended by Curle to include the estimation of laminar skin friction for the whole flow. The purpose of the following note is to compare the approximate methods of Curie and Skan and Curle with the numerical results given by the author for flow past a circular cylinder. It is found that there is remarkable agreement between these approximate methods and the exact numerical solutions. This indicates that these methods can be used widely, both on account of their simplicity and their accuracy.
Buckling of Tapered Rectangular Plates in Compression
Authors: Wittrick W. H. , Ellen C. H.
Published: July 2016

The problem considered is the buckling of a rectangular plate, tapered in thickness in a direction parallel to two sides, and uniformly compressed in that direction. Curves are presented showing the variation of buckling stress coefficient with the side ratio and the amount of taper, for each of two types of thickness variation, namely exponential and linear, and for each of two sets of boundary conditions, namely all edges simply-supported, and ends clamped and sides simply-supported. It is shown that, unlike the case of a uniform plate, there are no discontinuous changes of buckling mode.
Some Observations on the Compressive Buckling of Rectangular Plates
Authors: Wittrick W. H.
Published: July 2016

The problem considered is the buckling of a rectangular plate under uniaxial compression. The ends may be either both clamped, both simply-supported or a mixture of the two. The sides may be elastically restrained against both deflection and rotation with any stiffnesses whatsoever. It is shown that the curve of buckling stress coefficient versus side ratio can be deduced in a simple manner from that of a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength for an infinite strip with the same side conditions are known. Some correlations between the curves for the three types of end condition are discussed. It is also shown that if, for some given side ratio, the buckling mode is known, then it is always possible to deduce the rate of change of buckling stress coefficient with side ratio at that point. The argument is based upon an assumption which is shown to give very accurate results in a wide range of cases.
Some Remarks on Glauert's General Interference Theorem
Authors: Garner H. C.
Published: July 2016

After a retrospective discussion of Glauert's theorem concerning the wall interference on a small lifting aerofoil in a wind tunnel with mixed boundaries, a simple proof of the theorem is given for a tunnel having one rigid and one free boundary. It is shown that the theorem does not necessarily hold when there are two rigid walls and two free boundaries.
The Ludwieg Pressure-Tube Supersonic Wind Tunnel
Authors: Cable A. J. , Cox R. N.
Published: July 2016

A description is given of a supersonic pressure-tube wind tunnel which has been constructed at A.R.D.E. This is a blow-down tunnel which uses as a reservoir a long tube filled with gas under pressure. A quasi-steady supersonic flow is achieved by expanding in a convergent-divergent nozzle the subsonic flow behind rarefaction waves which propagate down the tube when a diaphragm at the nozzle exit is burst. The theory of the operation of the tunnel is given and calculations are made of the boundary-layer growth along the tube. Pressure-time records were obtained in the tube, and a high speed camera was used to obtain pictures of the flow round a model. Measurements also included a pitot-tube traverse of the nozzle exit, and the Mach number distribution was determined from the ratio of the pitot to the stagnation pressure. Tests showed that, as predicted, a constant stagnation pressure was obtained ahead of the nozzle, and it is considered that a tunnel of this type would be a cheap and simple way of obtaining an intermittent tunnel with adequate running time for many types of test, and capable of operating at a Reynolds number of more than 107 per inch at a Mach number of about 3·5.
Compressive Buckling of Infinite Strips with Elastically Restrained Edges
Authors: Wittrick W. H. , Bodley W. E.
Published: July 2016

It has been shown in another paper that the relation between the compressive buckling stress coefficient and side ratio for a rectangular plate with the sides elastically restrained against deflection and rotation can be obtained from the corresponding curve for a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength of the buckle are known for an infinite strip with the given side conditions. This paper presents these numerical values for infinite strips with a wide range of edge stiffnesses.
Flight Efficiency of Air-Breathing Engines
Authors: Bragg S. L.
Published: July 2016

The overall effective efficiency of a jet-propelled flight may be defined as the net useful work that is done in accelerating the vehicle, raising it to height and combating its drag, divided by the calorific value of the propellants used. The analysis presented here shows that for a single-stage vehicle this overall efficiency is equal to the integral of the fraction

with respect to each element of propellants used. In this expression u'is the effective jet velocity (allowing for jet deflection, this is √(1 + k2) times the actual exhaust velocity), υ the vehicle velocity, q the fuel/air ratio and H the calorific value of the fuel in dynamic units. The mean lift/drag ratio of the vehicle is taken as 1/k, so that the last three terms of the numerator represent the work lost in dragging, raising and accelerating each element of propellant to the range R, height h and flight velocity υ at which it is burnt. The fraction may therefore be considered as the efficiency with which that element of propellant is used with respect to the whole flight plan.

For advanced air-breathing projects—by-pass engines up to aircraft speeds around Mach 2 and ramjets between Mach 4 and 9—the analysis shows that the sum of the υ-dependent terms in the efficiency factor is practically constant. The potential energy term is insignificant in the normally accepted flight corridor. Thus the overall efficiency with which propellants are consumed in covering a range R1 at flight speed υ js closely approximated to by the fraction

and the useful work done by the mass mm of propellants is

The vehicle mass (including engine, payload, and so on) that can be dragged over the range R1 by unit mass of propellants can then be calculated.

Although such simplified expressions cannot substitute for the final detailed analysis of a projected flight plan, it is hoped that they will prove more useful in preliminary analysis than the figures based entirely on cruise performance which have often been quoted in the past.
The Effect of the Boundary Layer on the Lift of Finite Wings
Authors: Squire L. C.
Published: July 2016

The vorticity shed behind a finite wing has been studied and a condition found for steady circulation. This condition is then combined with three-dimensional boundary layer theory to find the lift of a finite wing. An example shows that on a thin ellipsoid of aspect ratio 6·37 the lift as found by the present method is 2 per cent lower than the lift obtained using a sectional boundary layer approach.
Aircraft Behaviour in a Vertical Gradient of Wind Velocity
Authors: Zbrożek J. K.
Published: July 2016

The stability of the phugoid motion of an aircraft in the presence of wind shear is investigated. The effect of the wind shear on the phugoid frequency increases with increasing aircraft speed and can be stabilising or destabilising, depending on the aircraft orientation relative to the wind shear. The destabilising effect of wind shear is alleviated by the stabilising effect of the density gradient of the atmosphere. At the most critical combination of speed and altitude a strong wind shear may lead to divergence, with a time to double amplitude of the order of 10-15 seconds.

A numerical study of the aircraft motion with controls fixed when descending through a wind profile similar to that in a jet stream indicates that the increase in the aircraft indicated speed can be of the same magnitude as, or larger than, the maximum wind velocity increment in the jet stream core. However, as the time to reach the excess speed is of the order of one minute, the actual behaviour of the aircraft strongly depends on the pilot's action and thus is not fully predictable by theoretical analysis.
The Effect of a Root Gap on the Aerodynamic Forces of a Slender Delta Wing in Oscillatory Pitching Motion
Authors: Judd M.
Published: July 2016

An investigation of the effect of a root gap is extended to the oscillatory pitching motion of a slender wing. Potential theory is used and the unsteady forces are shown to be reduced by the gap as drastically as the steady. These results cast doubt on measurements made by the technique of half-model testing. Viscous flow in the gap is discussed with reference to the possible types of model mount. The effect of viscosity may be to reduce the gap loss, but the extent of the improvement is uncertain.
Stresses Around a Reinforced Circular Hole Near a Reinforced Straight Edge
Authors: Davies G. A. O.
Published: July 2016

A solution is presented for the stresses in a half plane compactly reinforced along its straight edge and pierced by a reinforced circular hole in the vicinity of the edge. Numerical results are given for two cases of uniform applied tractions at infinity. In the special case of both boundaries unreinforced, the results obtained are in agreement with an existing solution by Mindlin.
Vibration of Non-Uniform Beams
Authors: Lindberg G. M.
Published: July 2016

A method of deriving a dynamic stiffness matrix for any non-uniform beam is presented. In particular, the case of a linearly tapered cantilever beam is considered, and excellent results are found with the use of only a few elements.
The Buckling Modes of a Longitudinally Stiffened Flat Panel
Authors: Martin D. W. , Cox H. L.
Published: July 2016

The complete analytical solution is presented to a problem formulated in an earlier issue of this publication.
Influence of Stiffener Thickness and Rivet Position upon the Effectiveness of Single-Sided Stiffeners on Shear Webs
Authors: Rockey K. C.
Published: July 2016

The paper presents the results of an experimental study of the buckling of transversely stiffened shear webs when the stiffeners have a thickness less than that of the web-plate.

It is shown that the effectiveness of such stiffeners is greatly influenced by two factors, the ratio of the thickness of the attached leg to that of the web-plate and the position of the connecting rivet. An empirical design rule relating these two factors is presented.
The Effect of Jet Entrainment on Lift and Moment for a Thin Aerofoil with Blowing
Authors: Wygnanski I . , Newman B. G.
Published: July 2016

Jet flap theory for thin aerofoils has been extended to include the effect of jet entrainment on the external flow when the jet is blown over the upper surface of the aerofoil. The effective camber of the aerofoil is increased by the sink effect due to entrainment and the increase of lift at zero incidence is proportional to the square root of the jet momentum coefficient. Formulae and charts are presented to facilitate the determination of the increments of lift and pitching moment due to this effect. The theory is shown to be in first-order agreement with the exact solution for a circular-arc aerofoil of small camber with distributed sinks on the upper surface.

The new theory is compared with four old sets and one new set of experimental data. It greatly improves the accuracy of prediction for cases where the incidence and flap angle are small. The new theory substantiates the usefulness of a small flap in applications of the jet flap principle.
The Flow Induced by Two-Dimensional and Axisymmetric Turbulent Jets Issuing Normally from an Infinite Plane Surface
Authors: Wygnanski I.
Published: July 2016

The flows induced by incompressible jets have been analysed for two-dimensional and axisymmetric jets emerging at right angles from an infinite plane surface. In particular, the pressure distribution on the surface has been predicted by replacing the jet with a line sink of variable strength. The theory takes account of the size of the blowing slot or nozzle and is in good agreement with experiment in both cases.
Applications of Linearised Characteristics to Sharp-Edged Conical Bodies
Authors: Squire L. C.
Published: July 2016

A review of existing work in the field of linearised characteristics suggests that the hypersonic approximation introduced by Chapkis should be adequate in many cases of practical interest; furthermore, of the methods available, this approximation requires least computation for the calculation of pressure distributions on a given shape at given speed. The application of this method to sharp-edged conical shapes shows good agreement with measured zero-incidence pressure distributions for a variety of shapes and a wide range of hypersonic parameter. The agreement is less good at incidence, possibly due to flow separations in the real flow.
On the Axisymmetrical Stress Concentration at an Eccentrically Reinforced Circular Hole in a Plate
Authors: Wittrick W. H.
Published: July 2016

This paper is concerned with the effectiveness of reinforcing a hole in a plate on one surface only. The particular problem considered is that of a circular hole in a plate of infinite extent, subjected to axially symmetrical tension at infinity, when the reinforcement consists of an annular plate on one surface. Because of the interaction between bending and stretching, the problem is highly non-linear and it has only been possible to solve it for certain limiting cases. The stress concentration factor depends on a dimensionless parameter proportional to the tension at infinity. It is shown that the stress concentration factor is increased, because of the eccentricity of the reinforcement, if the parameter is small, but for values of the parameter greater than a certain minimum the stress concentration factor is decreased. The results also make it quite clear that there is no possibility of obtaining reasonably accurate results by linearisation of the equations.
The Three-Shock Confluence on a Simple Wedge Intake
Authors: Henderson L. F.
Published: July 2016

Results obtained from previous studies of the three-shock confluence are applied to a simple wedge intake with the objective of obtaining a qualitative description of the flow for given initial conditions (M0, δ0). A simple mapping procedure is used, so that when M0, δ0 varies slowly and continuously the resulting effect on the shock geometry can be discussed in a systematic fashion. A number of special curves are computed to help classify various regions of initial conditions.
Some Aspects of the Design of Half-Ring Wing-Body Combinations with Prescribed Wing Loadings
Authors: Moore K. C. , Jones J. G.
Published: July 2016

This paper is concerned with half-ring wing-body combinations with prescribed wing loadings at supersonic speeds. Configuration shapes, their pressure distributions and their associated flow fields are discussed.
Shear Buckling of Clamped Infinitely Long Plates—Influence of Torsional Rigidity of Transverse Stiffeners
Authors: Rockey K. C. , Cook I. T.
Published: July 2016

The paper provides relationships between the buckling resistance of clamped transversely stiffened plates and the flexural rigidity of the stiffeners for various values of the ratio of torsional rigidity to flexural rigidity. Results are presented for four different stiffener spacings.
Design of Two-Dimensional Free Streamline Suction Slots for Parallel Channels
Authors: Lau W. T. F.
Published: July 2016

A general solution is obtained by using potential flow theory for the design of two-dimensional suction slots for parallel channels. These slots are formed by free streamlines and are so arranged that the channel walls are free from adverse pressure gradient. Where suction slots are intended for the control of boundary layers, the present solution can only be used as a basis for experiment. It is interesting to note that the results also suggest a new method for the design of diffusers by suction.
The Use of Excess Engine Exit Area Over Intake Area to Reduce Zero-Lift Drag at High Supersonic Speeds
Authors: Squire L. C.
Published: July 2016

At flight speeds above about M=2 the cross-sectional area of the fully-expanded jet nozzle tends to be larger than the intake streamtube. The principle of integrating this increase in area of the propulsion unit with the usable volume in order to reduce the after-body drag of the combination is discussed and calculations are made to establish the order of the effect. It is deduced that successful integration of this type can produce worthwhile increases in lift/drag ratio.
The Increase of Ablation Effectiveness by Surface-Active Compounds
Authors: Steverding B.
Published: July 2016

The heat of ablation of glassy materials can be improved by surface-active agents. The degree of improvement is more pronounced at high flight velocities and depends strongly on the coefficient of diffusion in the liquid layer. The analysis is carried out near the stagnation point of blunt bodies for steady state ablation.
The Growth of a Vortex in Turbulent Flow
Authors: Squire H. B.
Published: July 2016

The growth of a line vortex with time and the spread of a trailing vortex behind a wing due to turbulence are considered. It is shown that the eddy viscosity for this type of motion may be taken to be proportional to the circulation round the vortex and the solution is then similar to the solution for the growth of a vortex in laminar flow. The method is applied to calculate the distance behind a wing for which the trailing vortices will touch one another.
A Large Scale Fatigue Test of Aluminium Specimens
Authors: Bloomer N. T. , Roylance T. F.
Published: July 2016

There have been, in the past, many fatigue tests carried out on a variety of materials and components. These all indicate a wide scattering in the lives (measured by the number of stress cycles to failure) endured by nominally identical components subjected to nominally identical forces before failure occurs. To interpet this scattering several equations have been suggested as representing the statistical distribution functions that fit the lives obtained for individual types of component. Of these functions the log normal distribution function has been perhaps the most widely used. For the central regions of the probability distribution, i.e. about the mean, the log normal distribution and several others represent experimental results very closely indeed, but engineers and designers of all kinds dare not design on the mean fatigue life. They are concerned with specifications that either exclude the possibility of failure or admit only a very small probability of failure. It is thus with the accuracy with which the “lower tail” of the probability distribution curve fits the experimental results that they are concerned.

To assess the fit at this lower end for one type of component, a large number (about 1,000) of aluminium specimens have been tested and the corresponding lives plotted. The results are very interesting. They show clearly that the log normal distribution for this type of component and material is pessimistic for a probability of failure of less than 0·3. This result is felt by the authors to be of very great importance. It has further been shown that the use of the “one-sided censored distribution function”, used previously by one of the authors, gives a curve that will fit the lower results better than the complete log normal distribution would do.

It is with the testing procedure adopted, the specimens used, the distribution functions considered and the conclusions obtained therefrom that this paper is concerned.
The Effect of a Rear-Mounted Disc on the Drag of a Blunt-Based Body of Revolution
Authors: Mair W. A.
Published: July 2016

Experiments have shown that the drag of a body of revolution with a blunt base can be substantially reduced by mounting behind the body a disc of rather smaller diameter than the body. With a single disc the base drag was reduced by about 35 per cent and with two discs a reduction of 55 per cent was obtained. When the cavity between the body and the best single disc was filled in to form a solid boat-tailed afterbody there was an even greater reduction of drag.

A single disc mounted nearer to the body than the position giving low drag gave a large increase of drag with severely unsteady flow. The nature of the flow in both the low-drag and high-drag régimes is discussed.
On the Piston Motion of a Free-Piston Shock Tube
Authors: Peng Tzy C. , Elbert Theo. F.
Published: July 2016

The motion of a solid piston between the driver and test gases in a closed shock tube is studied. In particular, the piston stopping distance, i.e. the total length required to bring the piston to a stop, is calculated for various experimental conditions. Before the stop, the moving piston compresses the test gas, at first with its induced shock and then further with its own kinetic energy through the successive shock reflections. Thus, the moving piston can produce a reservoir of compressed gas with higher enthalpy than a shock of similar strength without the piston. Normal shock-wave theory for an ideal gas is used until the first reflected shock meets the piston. The subsequent shock reflections are approximated by a continuous compression in thermodynamic equilibrium. The calculated values for the piston stopping distance are found to compare favourably with the available experimental data, indicating that the approximations used are reasonable. Peak pressure and temperature of the compressed test gas are computed, and the effect of bleeding the gas reservoir through a nozzle is also included.
Discontinuities in Bent Plates
Authors: Redwood R. G.
Published: July 2016

A method of deriving the finite-difference equations to be applied at or near flexural discontinuities in plates subjected to bending is suggested. Such equations are presented for the case when a plate consists of two regions of different flexural rigidities, the boundary between the regions being formed by straight lines meeting at right angles.
Effects of a Source-Type Hypersonic Free Stream on the Flow Field about an Axisymmetric Cone
Authors: Savage Stuart B.
Published: July 2016

Most hypervelocity tunnels presently make use of conical or wedge type nozzles which produce source-type flow non-uniformities in the test section. The present paper considers the effects of such free-stream non-uniformities on the flow fields about slender axisymmetric cones. The inviscid flow is considered within the framework of the Newtonian expansion procedure of Cole and simple expressions are obtained for the flow field properties in the shock layer. This inviscid analysis predicts that a free-stream gradient of a magnitude typical of present hypervelocity test facilities can cause sizeable reductions in surface pressure and increased shock-layer thickness at the aft end of long slender conical models. The cone pressure, accounting for the viscous-inviscid interaction, is obtained by applying the inviscid analysis in tangent-cone fashion to the effective body (i.e. physical cone plus boundary-layer displacement thickness). Cheng’s simple equation is used to approximate the hypersonic boundary-layer development. Large increases in the boundary-layer thickness at the aft end of the model are predicted as a consequence of the source flow effects. The analyses agree well with experimental measurements of surface pressure and boundary-layer thickness made on a 5° half-angle cone tested in the Republic 24 inch Longshot I hypervelocity shock tunnel.
Forced Autorotat ion in the Rolling Motion of an Aeroplane
Authors: Walsh G. R.
Published: July 2016

The possible steady rates of roll of an aeroplane are determined in the case when inertia cross-coupling is present. This phenomenon not only changes the simple linear relationship between aileron angle and rate of roll, but may lead to more than one possible rate of roll for a given aileron angle. Simplified equations of motion are given for the cases in which the rolling takes place (a) from level flight, (b) during a pull-out manoeuvre. In both cases, these equations, which are non-linear, are solved numerically for typical examples. The static stability of the possible steady motions is considered in detail, and the dynamic stability is determined in the numerical examples.
Oscillating Slender Wings with Leading-Edge Separation
Authors: Randall D. G.
Published: July 2016

A theoretical study is made of the aerodynamics of wings executing simple harmonic oscillations. The wings considered are slender and infinite-simally thin; they may have curved leading edges and be cambered, but their cross sections must be straight lines. The value of the reduced frequency is assumed to be such that the flow is governed by the two-dimensional Laplace equation.

Leading-edge separation is simulated by a line vortex joined to the leading edge by a cut. The strength and position of the vortex and the values of the generalised forces can be determined by the theory. Results have been calculated for flat delta wings and a flat gothic wing; they are in reasonable agreement with experiment.
A Procedure for Automated Minimum Weight Structural Design: Part II: Applications
Authors: Gellatly Ronald A. , Gallagher Richard H.
Published: July 2016

This paper presents the application to a number of structural design problems of a procedure for determining minimum weight member sizes. Included are examples of trussed and stiffened plate structures and experience with computational times for a wide range of problem sizes.
The Nature of the Free-Stream Conditions Approaching an Oscillating Body in a Low Speed Wind Tunnel
Authors: Roberts B. W.
Published: July 2016

When correcting the measured unsteady aerodynamic forces experienced by an oscillating body for wind-tunnel interference, it is customary to assume that the free-stream conditions ahead of the model are invariant with time. For small, streamlined models oscillating with small amplitudes this assumption is substantially correct. However, for large variations in the drag force on the oscillating body this assumption is imprecise, particularly at low frequency parameters. In the present paper the flow at stations a long way removed from the body section is examined on the basis of the unsteady form of the Bernoulli equation. The predicted free-stream fluctuations are found to be in agreement with experiment.
Roll Control Techniques on Magnetic Suspension Systems
Authors: Goodyer M. J.
Published: July 2016

The various methods which axe available for controlling the rolling motions of a model suspended in an electro-magnet system are discussed. Data on the moment capability and damping achieved with some of the possible control techniques are presented, together with details of the roll control system adopted for the six-component magnetic balance which has been developed at Southampton University for an 8 in × 6 in supersonic wind tunnel.
Plate-Reinforced Holes
Authors: Davies G. A. O.
Published: July 2016

The problem considered is the theoretical analysis and design of reinforcement around holes in plane sheets subjected to prescribed stresses at infinity. The reinforcement is taken to be an extensive thin plate attached to the sheet rather than the usual “compact bead” placed around the inside of the hole. The optimum design of the hole and the reinforcement is treated in two ways, firstly as an attempt to produce a “neutral hole” and secondly, to achieve the smallest stress concentration with the minimum amount of reinforcement. It is found in two cases that the plate-reinforcement can be as efficient as the bead but that, for both types, the validity of the theory is doubtful just when they are most efficient.
Buckling of Longitudinally Stiffened Plates
Authors: Wah Thein
Published: July 2016

This paper investigates the effect of the torsional stiffness of the ribs on the buckling strength of stiffened plates compressed in the direction of the ribs. For the case of plates simply-supported on all sides, a closed form formula is derived for calculating the buckling load.
Similar and Asymptotic Solutions of the Incompressible Laminar Boundary Layer Equations with Suction
Authors: Zamir M. , Young A. D.
Published: July 2016

Similar solutions of the boundary layer equations for incompressible flow with external velocity u1 ∞ xm and suction velocity υw ∞ x(m-1)/2 are obtained for negative values of m, in the range −0-1 to −0-9, and a wide range of suction quantities.

The results are used, in combination with, existing solutions for positive m, to provide a guide to the ranges of m and suction parameter [(υw/u1√x] for which a general form of the classical asymptotic solution can be regarded as a good approximation to the exact solution.

It is shown that the values of both m and suction parameter are generally important in this comparison, but for values of the latter greater than about 8 the approximation is a very good one for all values of m considered. For m≃−0·14 the approximation is good (i.e. the error is less than about 1 per cent) down to values of the suction parameter as low as 1·0.
The Calculation of Three-Dimensional Turbulent Boundary Layers: Part II: Attachment-Line Flow on an Infinite Swept Wing
Authors: Cumpsty N. A. , Head M. R.
Published: July 2016

An earlier paper described a method of calculating the turbulent boundary layer flow over the rear of an infinite swept wing. It made use of an entrainment equation and momentum integral equations in streamwise and cross-flow directions, together with several auxiliary assumptions. Here the method is adapted to the calculation of the turbulent boundary layer flow along the attachment line of an infinite swept wing. In this case the cross-flow momentum integral equation reduces to the identity 0 = 0 and must be replaced by its differentiated form. Two alternative approaches are also adopted and give very similar results, in good agreement with the limited experimental data available. It is found that results can be expressed as functions of a single parameter C*, which is evidently the criterion of similarity for attachment-line flows.
Transitional and Turbulent Boundary Layers on a Cold Flat Plate in Hypersonic Flow
Authors: Richards Bryan E.
Published: July 2016

An experimental investigation of natural transition and turbulent boundary layers on a cold flat plate in hypersonic flow was carried out in the Imperial College Gun Tunnel. Studies were also made of the effects of both two- and three-dimensional roughness elements including vortex generators.

Results indicate that the Reynolds number based on the end of transition consists of two separate parts. These are the Reynolds numbers based respectively on the position of the apparent origin of the transition region behaviour, Ri, and on the length of the transition region measured from this origin. Ri is shown to be independent of unit Reynolds number for a sharp leading-edge model, and by correlations of other published data to vary little with Mach number. This origin is perhaps the most relevant point when comparisons are made between experiment and classical stability theory. The variation of the heat transfer rate during the transition region is compared with findings at low speed and shown to be similar to that expected from the turbulent spot concept of Emmons. The measured variation of the length of the transition region (x) from this origin gives an explanation for the unit Reynolds number effect on transition, and the rapid increase of transition Reynolds number with Mach number in hypersonic flow. The effect of bluntness on these factors is discussed.

The virtual origin of the turbulent boundary layer is shown to lie close to the measured beginning of transition. At these high Mach number and low wall temperature conditions experimental values of heat transfer and values of skin friction coefficient derived from the estimated momentum thickness growth in the turbulent region are found to be appreciably higher than predictions by present theories.

Roughness trips were found to bring the whole transition region forward. Only small differences in the measured boundary layer thickness, shape and heat transfer rates in the turbulent region (referenced to the estimated virtual origin in each case) were found after natural and forced transition. The transition point locations on a flat plate with either spherical roughness elements or vortex generators were found to agree with values predicted by the method of Potter and Whitfield as modified by Luxton to account for the effects of heat transfer.
Reinforced Sheets for Load Envelopes Which Combine Tension and Shear
Authors: Harris G. Z.
Published: July 2016

An exact analysis is made of reinforced sheets having three fibre directions using netting analysis. Load envelopes of shear combined with both uniaxial and biaxial tension are assumed and optimum fibre arrangements are determined on the assumption that limits exist on the compressive and tensile forces which may be developed in a fibre. Such optimum fibre arrangements are compared with the best-arranged isotropic reinforced sheets and with hypothetical solid sheets having the same properties as the fibres. Elastic constants are derived for the optimum systems. The total allowable load envelopes of the optimum arrangements are found and are related to the prescribed load envelopes.
Natural Frequencies of Long Tapered Cantilevers
Authors: Carnegie W. , Thomas J.
Published: July 2016

The effect of depth taper on the flexural vibration characteristics of a beam of uniform width is investigated in this paper. The frequency parameters and mode shapes for the first five modes of vibration of tapered beams are presented for a wide range of depth taper. The Euler-Bernoulli equation of a beam is reduced to an eigenvalue problem and its eigenvalues and eigenvectors are obtained by using a digital computer. The theoretical results are compared with those of other authors and with the experimental results.
The Stresses Around Holes in Plane Sheets
Authors: Howard I. C. , Morley L. S. D.
Published: July 2016

This paper describes the application of a previously published variational method to the solution of problems of holes in plane elastic sheets and is used to obtain numerical values for the specific case of an elliptic hole in an infinite sheet under tension at infinity. Two kinds of boundary condition at the hole are discussed. The first is that when the hole is unreinforced and stress free, and the second that when the hole is uniformly reinforced by a compact member. The results of the calculations are compared with those from known solutions to the problem, and the accuracy of the present method is investigated. These results provide a useful background to wider application of the method.
Buckling of a Long Flat Panel with a Series of Equidistant Longitudinal Supports in Combined Longitudinal Compression and Shear
Authors: Wittrick W. H. , Curzon P. L. V.
Published: July 2016

The main purpose of this paper is to illustrate the use of the stability functions for long plates in combined compression and shear defined in a previous paper by the authors. The panel is supported on its two edges and on a series ofNintermediate simple supports. Each of the two edges is either clamped or simply-supported and numerical results are given for each of the three possible combinations, with varying numbers of supports. In all cases it is found that a simple parabolic interaction formula between shear and compression is extremely accurate. Also simple approximate formulae are given for calculating the wavelength of the buckle and the lead of the nodal lines for any combination of compression, shear, edge conditions and number of supports.
The Turbulent Wall Jet in an Arbitrary Pressure Gradient
Authors: Gartshore I. S. , Newman B. G.
Published: July 2016

A method for calculating the growth of a turbulent wall jet in streaming flow has been developed. The flow is assumed to be two-dimensional, incompressible and over a plane, smooth wall. Downstream variations of pressure are permitted and separation in an adverse pressure gradient may be predicted. The method incorporates procedures for matching the flow to that at the blowing slot, although it is postulated that the upstream boundary layer there is thin enough that the wall jet develops without an unmixed wake (i.e. there is not a minimum in the mean-velocity profile).

The method incorporates four integral momentum equations taken from the wall to various points in the flow. The calculation of the outer shearing stress, although empirical, is based on the large-eddy equilibrium hypothesis and therefore has some foundation. The remaining empiricism in the method is based on measurements in self-preserving wall jets.

The method has been used to predict the jet-momentum coefficient required to suppress separation over a trailing-edge flap attached to a thin aerofoil. Plausible curves have been obtained Using assumed values of upstream boundary layer at the slot. Of some practical interest is the indication that large savings in power are possible if the upstream boundary layer is removed. This indicates that blowing combined with upstream suction, or multiple-slot blowing, may give useful savings in the application of blowing to prevent separation.
A Bending Theory for Multi-layer Anisotropic Conical Shells
Authors: Liaw Boen-Dar
Published: July 2016

The governing equations for bending of truncated conical shells with multi-layer anisotropic construction are developed by a variational method. The shell is considered to consist of an arbitrary number of alternating soft and hard layers. It is assumed further that the n hard membrane layers are isotropic and may possess different elastic properties, while the (n-1) soft core layers are orthotropic in general and may take transverse shear only. The variations of stresses across the membranes are neglected, as are the surface-parallel stresses in the cores. These assumptions are consistent with those usually employed in single-core sandwich shells. The energy functional is formulated with the stresses considered as independent variables. The stresses are also dependent variables defined in the set of two curvilinear co-ordinates defining the surface of the shell. The stress resultants are introduced as constraint conditions utilising Lagrange multipliers. Successful definition of an elastic neutral surface ensures the uniqueness of shell constants and the equations obtained may be in a form comparable to that of classical shell theory. The system of equations is reduced to a form where Galerkin’s method can be applied directly.