In Part 1 expressions are derived for the coupled torsional, extensional and flexural stiffnesses of a fibre composite tube, such as a helicopter blade, which is subjected to torsion, longitudinal tension, chordwise and flapping bending moments and shear. The theory is an extension of Batho-Bredt engineering analysis and is valid for a cylindrical tube of arbitrary cross-section with an arbitrary circumferential distribution of fibre composite plies. Particular attention is paid to the coupling effects in which an asymmetric fibre lay-up results in a twisting of the tube under bending and/or tension. Consideration is also given to the influence on the stiffness characteristics of an initial twist in the tube.

In Part 2 the analysis of Part 1 is developed numerically for tubes representative of GFRP blades. Static and dynamic aspects are considered which pave the way for aeroelastic tailoring studies of such blades.

The presence of numerical noise in engineering design optimisation problems inhibits the use of many gradient-based optimisation methods. This numerical noise may result in the inaccurate calculation of gradients which in turn slows or prevents convergence during optimisation, or it may promote convergence to spurious local optima. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expense of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimisation. To address these issues, a procedure has been developed to create noise-free algebraic models of subsonic and supersonic aerodynamic performance quantities, for use in the optimisation of high-speed civil transport (HSCT) aircraft configurations. This procedure employs methods from statistical design of experiments theory and response surface modelling to create the noise-free algebraic models. Results from a sample HSCT design problem involving ten variables are presented to demonstrate the utility of this method.

Water tunnel flow visualisation experiments on a slender delta wing have revealed some new phenomena connected with vortex breakdown. Vortex breakdown hysteresis has been found, there being two steady flow states at some incidences, one with breakdown on the wing and one without. The formation of vortex breakdown has been studied and found to be a non-axisymmetric instability. It is suggested that pressure gradient plays a more general part in the phenomenon than has been thought hitherto.

This paper reports an experimental investigation into the stagnation bubbles found in the shock layers of some supersonic jets impinging on perpendicular flat plates at small nozzle-to-plate distances. The experiments used twelve contoured nozzles within the Mach number range 1.42 to 2.83. Surface pressures were measured on the plate and free-jet pitot pressure distributions were obtained at the level of the centre of the plate shock. Schlieren pictures were taken of both impinging and free jets. It was found that the bubbles result from the interaction of the plate shock with very weak shock waves which are produced in the jet either by small imperfections in the nozzle wall or by slight inaccuracies in the design or production of the nozzle contour. The bubbles can be eliminated by suitable improvements to the nozzle. Other anomalous flows produced by shock interactions are described and explanations offered. It is shown that the bubbles sometimes encountered at close plate spacings with conical nozzles are also due to shock waves. However, for wide-angled nozzles, internal shocks can be an inherent part of the flow from the nozzle and the bubbles which they produce are thus an inherent part of the impingement flow. From physical arguments concerning the main factors involved in producing a bubble, a parameter is constructed whose values are shown to be a good criterion for whether a bubble occurs or not.

The pure bending of a rectangular beam about an axis parallel to a principal axis of its cross-section is well understood if its depth d is comparable in magnitude with its breadth b. The usual theory, noticing the geometrical fact that at any cross-section the longitudinal strains of filaments of the beam are proportional to the distances of the filaments from some neutral axis parallel to the axis of bending, postulates that the longitudinal stresses will vary in the same way.

Peridynamics is a recently proposed continuum theory based on a non local approach and formulated with integral equations. The theory is suitable for dealing with crack propagation in solid materials. The original peridynamic formulation regarded dynamic problems and was adapted to the static case mainly using a relaxation method by introducing a substantial amount of numerical damping in the time integration. In the present work the implementation of the theory within an implicit code for static crack propagation phenomena based on the Newton-Raphson method is presented and applied to several examples of static crack propagation equilibrium problems. Results obtained with the newly developed procedure are presented for various structural configurations, with different boundary and load conditions and quantitatively compared to published data.

A class of delta wings is considered, whose under-surface has an inverted-V, or inverted-W, cross section of such a form that, at the “design” Mach number and incidence, the shock waves formed are plane. The geometry of the shock-wave system and surface is described briefly, and comments made about the utility of the concept in relation to hypersonic flow studies.

It was easy for me to choose a subject for this lecture. First, turbulence is an important part of engineering fluid dynamics which has not so far been treated in the Reynolds-Prandtl lectures; secondly, it is the most obvious link between the careers of our two heroes; and thirdly it is the only scientific subject on which I am even remotely qualified to lecture before such a distinguished audience. The first and second propositions are sufficiently demonstrated by the annual consumption of something of the order of 1010kg of kerosene to overcome the effects of Reynolds’ stresses in Prandtl’s boundary layers. Have any two human beings ever had such a spectacular memorial? (Yes, Lanchester and Prandtl, to whose induced drag we sacrifice another 1010kg of fuel each year.)

This paper gives details of theoretical and experimental investigations into the behaviour of simply-supported uniformly compressed square and rectangular plates with central circular holes. The theoretical analysis employs an approximate approach using a combination of Rayleigh-Ritz and finite-element methods. The experimental investigation consisted of a number of experiments on plates with hole diameters from one- to seven-tenths of the plate width. Agreement between experiment and theory is shown to be good at buckling. In the post-buckling range it is found that the theoretical analysis is reasonably accurate for small holes, but loses accuracy when dealing with large holes.

Existing experimental data on the occurrence of attached flow around the leading edges of swept plane thin wings is summarised. It is shown that the change from separated to attached flow occurs while the Mach number normal to the leading edge is subsonic and that the Mach number required for the change increases with incidence. It is also shown that the Mach number and incidence conditions which hold on the boundaries dividing the two types of flow on wings with straight edges also apply locally at points on the leading edges of “Gothic” wings. The implications of this result on the flow over general curved-edge wings is briefly discussed.

The supersonic combustion ramjet, or scramjet, is the engine cycle most suitable for sustained hypersonic flight in the atmosphere. This article describes some of the challenges facing scramjet designers, and the methods currently used for the calculation of scramjet performance. It then reviews the HyShot 2 and Hyper-X flight programs as examples of how sub-scale flights are now being used as important steps towards the development of operational systems. Finally, it describes some recent advances in three-dimensional scramjets with application to hypersonic cruise and multi-stage access-to-space vehicles.

The general technique for rendering approximate solutions to physical problems uniformly valid is here applied to the simplest form of the problem of correcting the theory of thin wings near a rounded leading edge. The flow investigated is two-dimensional, irrotational and incompressible, and therefore the results do not materially add to our already extensive knowledge of this subject, but the method, which is here satisfactorily checked against this knowledge, shows promise of extension to three-dimensional, and compressible, flow problems.

The conclusion, in the problem studied here, is that the velocity field obtained by a straightforward expansion in powers of the disturbances, up to and including either the first or the second power, with coefficients functions of co-ordinates such that the leading edge is at the origin and the aerofoil chord is one of the axes, may be rendered a valid first approximation near the leading edge, as well as a valid first or second approximation away from it, if the whole field is shifted downstream parallel to the chord for a distance of half the leading edge radius of curvature ρL. It follows that the fluid speed on the aerofoil surface, as given on such a straightforward second approximation as a function of distance x along the chord, similarly is rendered uniformly valid (see equation (52)) if the part singular like x-1 is subtracted and the remainder is multiplied by .

In response to the need for ground testing facilities for super orbital re-entry research, a small scale facility has been set up at the University of Queensland to demonstrate the Superorbital Expansion Tube concept. This unique device is a free piston driven, triple diaphragm, impulse shock facility which uses the enthalpy multiplication mechanism of the unsteady expansion process and the addition of a secondary shock driver to further heat the driver gas. The pilot facility has been operated to produce quasi-steady test flows in air with shock velocities in excess of 13 km/s and with a usable test flow duration of the order of 15 μs. An experimental condition produced in the facility with total enthalpy of 108 MJ/kg and a total pressure of 335 MPa is reported. A simple analytical flow model which accounts for non-ideal rupture of the light tertiary diaphragm and the resulting entropy increase in the test gas is discussed. It is shown that equilibrium calculations more accurately model the unsteady expansion process than calculations assuming frozen chemistry. This is because the high enthalpy flows produced in the facility can only be achieved if the chemical energy stored in the test flow during shock heating of the test gas is partially returned to the flow during the process of unsteady expansion. Measurements of heat transfer rates to a flat plate demonstrate the usability of the test flow for aerothermodynamic testing and comparison of these rates with empirical calculations confirms the usable accuracy of the flow model.

This paper provides the basis for a very general approach to the determination of initial buckling stresses of long stiffened panels in uniform longitudinal compression. The panels are assumed to consist of a series of long flat strips, rigidly connected together at their edges, as in panels with top-hat or Z-section stringers, or in sandwich panels with corrugated cores. Whatever the buckling mode, the individual flats are subjected, just after buckling, to sinusoidally varying systems of both out-of-plane and in-plane edge forces and moments, superimposed on the basic state of uniform compression. The stiffness matrices corresponding to these sinusoidal edge loads are derived, taking account of the destabilising effect of the basic longitudinal compressive stress, not only in the out-of-plane but also in the in-plane deformations. For the latter purpose a non-linear theory of elasticity is used. The application of these stiffness matrices to specific panels is briefly described. All possible modes are incorporated within one determinantal equation. For panels with identical stiffeners spaced at equal intervals, the order of the determinant is independent of the number of stiffeners.

This paper describes measurements made in the regions of separated flow associated with three simple sharpedged two-dimensional geometries, a rear-facing step, a front-facing step and a rectangular block. The use of the pulsed-wire anemometer made possible the measurement of the three components of mean velocity and turbulence; earlier techniques, such as the hot-wire anemometer, were not well suited to the accurate determination of these quantities either in regions of continually reversing flows such as the re-circulatory zone or in regions of very high turbulence such as the shear layers bounding these zones. Supplementary measurements of surface pressure and shear stresses are also presented and comparison is made between these shear layers and the plane mixing layer. The work forms the first part of an extended programme for the investigation of bluff body flows but its principal immediate value will probably help in providing data with which to test the validity of mathematical models of turbulence as applied to re-circulating flows.

The flow generated by a synthetic jet actuator with a circular orifice is investigated experimentally and computationally. The experimental data and computational predictions are in fair to good agreement with each other and with the theory for a steady turbulent jet. It is found, however, that the synthetic jet establishes itself much more rapidly than the steady jet, primarily because of turbulent dissipation. The oscillatory nature of synthetic jet flow also gives rise to a much greater entrainment of ambient fluid compared with the case of a steady jet. Finally, self-similarity seems to be established when the oscillations introduced by the actuator are reduced to negligible levels.

This paper is the first of a series of three which are concerned with the subject of “ hysteretic damping.” This type of damping, in a simple system with one degree of freedom, is like the familiar “ viscous damping ” in that it implies a resisting force which is in phase with velocity; but it is unlike viscous damping in that the magnitude of the force is not proportional to the velocity but to the displacement. When a system has n degrees of freedom, hysteretic damping implies that damping forces exist which are proportional to relative displacement but which are in phase with relative velocity.

From a physical standpoint, hysteretic damping may give a better representation of the facts when the damping arises from the internal friction of solid materials. On the side of theory, it raises considerations which it is the purpose of these three papers to elucidate. It may be said, at the outset, that the notion of hysteretic damping raises no great mathematical difficulty; on the contrary, a main reason for presenting the theory is that it appears to allow of a much simpler discussion (than does viscous damping) of the nature of steady damped oscillation of systems having n degrees of freedom.

In the first paper, the purpose is discussed of mathematical theories of damping in vibration theory. It is concluded that the theory of “ hysteretic damping ” is a useful one since it provides an alternative to the fiction of “ viscous ” damping while retaining the mathematical linearity of equations of motion. The word “ hysteretic” is proposed for use in this sense instead of the previously used adjective, namely “ structural.” “ Complex damping ” is related to hysteretic damping in a way which is explained.

The theory is given for forced oscillations of a system with one degree of freedom. It is shown that free vibration cannot be treated satisfactorily unless the definition of hysteretic damping is widened in some way to cover non-harmonic motion.

Blade-element models are the most common models for the analysis of propeller aerodynamics, performance calculations and propeller design. In spite of their simplicity these models are very efficient and accurate. Blade-element models use the local induced velocities as an input thus they should be combined with another model in order to calculate these induced velocities. Various models are used for the calculation of the induced velocity, where the most popular ones include: momentum, simplified-momentum, lifting-line (prescribed and free wake), and vortex (McCormick and Theodorsen) models. The paper describes the various models, compares their results and discusses the advantages and disadvantages of each one. The results indicate that the Bladeelement/simplified-momentum model offers very good accuracy together with high efficiency. For propeller performance calculations during steady axial flight, where most of the cross-sections do not experience stall, detailed and complicated models for calculating the induced velocities do not show advantages over the simple bladeelement/simplified-momentum model,

The full equations of motion for the flow of a viscous fluid have proved too complicated for any general solution to be obtained. It is to be doubted if, in. the near future, the problem of fluid motion will be solved in a general manner, although solutions for a few special cases may be found. In view of this it is of some value to investigate experimentally certain cases which are likely to prove of mathematical interest at a later date; this paper deals with such a problem. By means of the results obtained experimentally the mathematical analysis may be guided along the right lines and a satisfactory analytical solutioa of the problem be obtained.

The instrument used in exploring the fluid motion has a special interest of its own as it may prove of use in further aerodynamical investigations where the flow is of three–dimensional character. The development of this instrument, and its performance when tested, are described in Part I.

The experiments for the measurement of the forces on the spinning sphere are described in Part II.

In this paper the development and flight testing of flapping-wing propelled, radio-controlled micro air vehicles are described. The unconventional vehicles consist of a low aspect ratio fixed-wing with a trailing pair of higher aspect ratio flapping wings which flap in counterphase. The symmetric flapping-wing pair provides a mechanically and aerodynamically balanced platform, increases efficiency by emulating flight in ground effect, and suppresses stall over the main wing by entraining flow. The models weigh as little as 11g, with a 23cm span and 18cm length and will fly for about 20 minutes on a rechargeable battery. Stable flight at speeds between 2 and 5ms–1 has been demonstrated, and the models are essentially stall-proof while under power. The static-thrust figure of merit for the device is 60% higher than propellers with a similar scale and disk loading.