This paper presents a numerical method, derived directly from the basic differential equations of motion and expressed in the form of recurrence-matrix of finite differences, that can be generally applied to all multi-degree-of-freedom structures subjected to dynamic forces or forced displacements on any masses at any instants of time. The movements of the system may be described by any form of generalised co-ordinates.

Wind tunnel measurements have been made of the attachment-line boundary layer on a swept wing. The combination of a 4-5 in (114 mm) nose radius and 60° angle of sweep enabled a wide range of values of the parameter V2/(v dU/dx) (denoted here by C*), to be covered, and gave a thick enough boundary layer for the velocity profiles to be accurately measured. Pitot traverses were performed for values of C* from 0·59 × 105 to 3·7 × 105. Without a trip wire fitted the attachment-line flow was laminar over the full range and the measured velocity profiles agreed closely with the theory for an infinite swept wing. With a large trip wire fitted, a transition régime was observed in the range 0·6 × 105 < C* < 1·4 × 105, and at higher values of C* the flow was fully turbulent and showed good agreement with the earlier calculations of Cumpsty and Head. Preston tubes were used for skin friction measurements in fully turbulent conditions and a hot wire was used to explore the development of turbulence in the transition régime.

Transverse curvature effects in axi-symmetric flow on a circulai cylinder are discussed and it is deduced that for small δ/a, where δ is the boundary layer thickness and a is the cylinder radius, transverse curvature effects are small, for δ/a = 0(1) the effect is felt mainly in the outer region and for δ/a » 1, both the inner and the outer regions are affected. It is argued that the last case can only be achieved experimentally in the laboratory if the radius Reynolds number Ra= U1a/v is small and the streamwise Reynolds number Rx=U1xlv is large, implying x/a large. New experimental data are presented for this case. The data show that both the mean and turbulent flow field scale on outer variables throughout the layer and, for Ra≥455, exhibit Reynolds number independence. No logarithmic region is found in the mean profiles, a result which is echoed by the absence of a shoulder in the streamwise turbulence profiles which clearly evidence that the flow in the layer is fully turbulent. A flow model is suggested, in physical terms, to explain the very high turbulence levels found close to the cylinder at values of Ra which should, according to stability theory, be bordering on laminar flow.

The reduction in stress concentration factors resulting from the introduction of an interference-fit pin in a circular hole in a flat plate to which a simple tension is applied has already been recorded. The same result is found to occur to an equally marked extent, and qualitatively in a very similar way, when the load is applied to the pin itself. When varying loads are applied to the pin or the plate, the effect of the interference is to produce a rise in the mean stress level at critical points on the hole boundary with a marked fall in the oscillatory stress. There appears to be an optimum value for the “interference stress” for given applied loading conditions at which the endurance of the plate will have its highest value.

When loads are applied simultaneously to pin and plate the critical stress on the hole boundary is found to be the mean of the stresses which would be produced by the total load applied separately to the pin and to the plate.

An exact integral formulation of the two-dimensional full potential equation is presented. The well developed standard surface panel method based on the linear Prandtl-Glauert equation is extended by means of sources in the field surrounding the configuration, allowing the calculation of transonic flows.

A major attraction of the Field Panel Method is that solutions can be obtained using standard surface panelling together with a field grid which has no special form. The surface panels are used to satisfy the boundary conditions so that the field grid does not have to be surface-fitted which is a requirement for existing field methods. Further, the grid need only be in a region close to the configuration where nonlinear compressibility effects are non-negligible and need not extend to the far field as generally required. Grid generation is therefore trivial allowing solutions for arbitrary configurations. Convergence, especially for flows with shock waves, is enhanced by use of a modified Approximate Factorisation scheme. Results for single aerofoils are compared with Garabedian-Korn solutions and show good agreement; and to demonstrate the ease of grid generation, results for multicomponent aerofoils are also presented. Finally, an outline is given of how the method can be extended to threedimensions.

The work was carried out in conjunction with the Department of Applied Mathematics, University of Leeds together with Procurement Executive, Ministry of Defence.

In the coming century, the impact of air travel on the environment will become an increasingly powerful influence on aircraft design. Unless the impact per passenger kilometre can be reduced substantially relative to today’s levels, environmental factors will increasingly limit the expansion of air travel and the social benefit that it brings. This essay considers the three main impacts, noise, air pollution around airports and influence on climate change. Of the three, impact on climate change is taken to have the greatest long-term importance and is discussed at the greatest length. It is argued that, of the three main contributors to climate change from aircraft – CO2 emissions, NOX emissions and the creation of persistent contrails – it is the last two which are the most promising targets. Ways of reducing the impacts of these two are discussed and it is noted that, in each case, the best environmental result is likely to entail some increase in CO2 emissions. It follows that regulatory or economic measures to reduce impact on climate should be framed so as to do just that. Measures framed purely in terms of CO2 emissions are likely to be counter-productive. Nevertheless, the design of aircraft to reduce fuel burn and hence CO2 emission remains a key long-term objective; the essay considers the potential offered by new technology and new design concepts in this arena.

An appropriate introduction to the topic of this lecture is the following comment taken from Cierva's third and last lecture presented before this Society in 1935:

“Perhaps the most irritating of the secondary difficulties met with in the Autogiro development have been those of a dynamical nature. The dissymmetry of speed on both sides of the rotor produces periodical variations in the lift and drag…“

The Fourth Cierva Memorial Lecture, which it is my privilege to present, is concerned with these periodic variations and their contribution to what remains one of the most irritating problems in rotary wing design.

Base cavities (hollow extensions mounted behind the rear end of a bluff body) are known to reduce substantially the aerodynamic drag of two-dimensional bodies. For axisymmetric bodies their effect is not well established, and the objective of this work was to assess their drag-reducing potential. Experiments were performed using three different types of base cavities, one solid walled and two ventilated, each with six different depths ranging from 0.1 to 0.9 body diameters. All three types of cavities reduced the body drag for small cavity depths, with a maximum drag coefficient reduction of 0.027 being obtained with a ventilated cavity 0.2 diameters deep. The reductions are an order of magnitude lower than those reported for two-dimensional bodies, but are achieved with a much shorter cavity depth. Although the ventilated cavities had a beneficial effect for small depths, at large depths (greater than 0.5 diameters) they had an opposite effect – a very large drag increase. The cause of this increase is as yet not understood. Hot-wire investigation revealed that base cavities suppress wake periodicity. For cavities of small depth this correlated with a reduction in drag, but for large cavity depths the trends of the intensity of the periodic motion and of drag were not always the same.

Efforts to develop the next generation of aircraft with ever-increasing levels of performance – higher, farther, faster, cheaper – face great technical challenges. One of these technical challenges is to reduce structural weight of the aircraft. Another is to look to aircraft configurations that have been unrealizable to date. Both of these paths can lead to a rigid flex coupling phenomenon that can result in anything from poor flying qualities to the loss of an aircraft due to flutter. This has led to a need to develop an integrated flight and aeroelastic control capability where structural dynamics are included in the synthesis of flight control laws. Studies have indicated that the application of an integrated flight and aeroelastic control approach to a SensorCraft high-altitude long-endurance vehicle would provide substantial performance improvement(1,2). Better flying qualities and an expanded flight envelope through multi-flutter mode control are two areas of improvement afforded by integrated flight and aeroelastic control. By itself, multi-flutter mode control transforms the flutter barrier from a point of catastrophic structural failure to a benign region of flight. This paper discusses the history and issues associated with the development of such an integrated flight and aeroelastic control system for the X-56A aircraft.

The development of adaptive morphing wings has been individuated as one of the crucial topics in the greening of the next generation air transport. Research programs are currently running worldwide to exploit the potentiality of morphing concepts in the optimisation of aircraft efficiency and in the consequent reduction of fuel burn. Among these, SARISTU represents the largest European funded research project which ambitiously addresses the challenges posed by the physical integration of smart concepts in real aircraft structures; for the first time ever, SARISTU will experimentally demonstrate the structural feasibility of individual morphing concepts concerning the leading edge, the trailing edge and the winglet on a full-size outer wing belonging to a CS-25 category aircraft. In such framework, the authors intensively worked on the definition of aeroelastically stable configurations for a morphing wing trailing edge driven by conventional electromechanical actuators. Trade off aeroelastic analyses were performed in compliance with CS-25 airworthiness requirements (paragraph 25.629, parts (a) and (b)-(1)) in order to define safety ranges for trailing-edge inertial and stiffness distributions as well as for its control harmonics. Rational approaches were implemented in order to simulate the effects induced by variations of trailing-edge actuators’ stiffness on the aeroelastic behaviour of the wing also in correspondence of different dynamic properties of the trailing-edge component. Reliable aeroelastic models and advanced computational strategies were properly implemented to enable fast flutter analyses covering several configuration cases in terms of structural system parameters. Already available finite elements models were processed in MSC-NASTRAN® environment to evaluate stiffness and inertial distributions suitable for the stick-equivalent idealisation of the reference structure. A parametric stick-equivalent model of the reference structure was then generated in SANDY3.0, an in-house developed code, that was used for the definition of the coupled aero-structural model as well as for the solution of aeroelastic stability equations by means of theoretical modes association in frequency domain.

Obtained results were finally arranged in stability carpet plots efficiently conceived to provide guidelines for the preliminary design of the morphing trailing-edge structure and therein embedded actuators.

The historical trends of reduction in fuel consumption and emissions from aero engines have been mainly due to the improvement in the thermal efficiency, propulsive efficiency and combustion technology. The engine Overall Pressure Ratio (OPR) and Turbine Inlet Temperature (TIT) are being increased in the pursuit of increasing the engine thermal efficiency. However, this has an adverse effect on engine NOx emission. The current paper investigates a possible solution to overcome this problem for future generation Very High Bypass Ratio (VHBR)/Ultra High Bypass Ratio (UHBR) aero-engines in the form of an Inter-stage Turbine Burner (ITB). The ITB concept is investigated on a next generation baseline VHBR aero engine to evaluate its effect on the engine performance and emission characteristics for different ITB energy fractions. It is found that the ITB can reduce the bleed air required for cooling the HPT substantially (around 80%) and also reduce the NOx emission significantly (>30%) without penalising the engine specific fuel consumption.

A decade has elapsed since triangular elements under constant strain and stress were independently introduced within the matrix Displacement Method by the Turner group at Boeing and the Aeronautical Structures Department at Imperial College. They proved a considerable success in the practical analysis of complex membrane shapes as occur in modern aircraft wings. However, the original formulation based on a local cartesian system of axes and the classical concept of stress and strain inevitably leads to an unsymmetrical and aesthetically (as well as computationally) unfavourable expression for the stiffness matrix k. Moreover, the method was restricted to isotropic media. The necessity of extending the theory to finite displacements ultimately showed the inadequacy of the past approach and guided the writer to the creation of new concepts, e.g. the natural stiffness of an element. This natural stiffness, which ignores the rigid body motions and is hence of dimensions (3 X 3) for a triangle with three nodal points, relates in a concise manner the nodal force components parallel to the sides and the elongations of the sides themselves. A powerful tool in its derivation and further development was a new definition of stress and strain vectors which excludes shearing contributions and only works with direct components parallel to the sides. The idea has also been extended to tetrahedra and many standard elements which are incorporated as a basic feature in the structural language ASKA (Automatic System for Kinematic Analysis) developed at ISD by the Applied Programming Group under Dr. H. Kamel. These fundamental ideas were emphasised in the author's recent lecture to the Society.

On unswept wings, or wings with small amounts of sweep, the favourable pressure gradient round the leading edge, where the flow is rapidly accelerated away from the stagnation line, ensures a certain amount of laminar flow, provided the wing surface is sufficiently smooth. On highly swept wings, however, it has been found that turbulent flow can exist on the attachment line itself and there are therefore no naturally occurring regions of laminar flow. This trouble arises from the turbulence at the root of the wing, which sweeps along the attachment line. If the Reynolds number of this turbulent attachment line boundary layer is greater than some critical value, the whole attachment line boundary layer remains turbulent and the complete wing is contaminated. But if the Reynolds number is below the critical value, the turbulence decays along the leading edge and the boundary layer on the attachment line reverts back to the laminar state. This situation arises when the leading edge radius is small and the wing is only slightly swept. The attachment line boundary layer Reynolds number, Rθ, is given by the following equation:

In this paper lower bounds are obtained for the intensity of the sonic bang resulting from a slender aircraft flying straight and level at supersonic speeds. The lower bounds are obtained for an aircraft subject to various constraints on its total lift, volume, area distribution and centre-of-pressure position. The work described proves the results quoted in an earlier paper, corrects the results given in that paper for the general configuration, and extends the results to cover more constraints, mainly the centre-of-pressure position.

A powerful mechanism for the generation of secondary flow, which does not rely on viscous or turbulent stress, is lateral skewing of a shear layer such as that encountered by the body boundary layer in a wing/body junction. For a given entry shear, the characteristics of the secondary flow (a horse-shoe vortex) will depend on the wing nose shape. The effects of three wing nose shapes on the size, position and strength of the horse-shoe vortex have been studied in low-speed flow. As expected, the vortex size and strength increased with nose bluntness; quantitative data describing this effect are presented in this paper. The results include contours of streamwise velocity and secondary velocity plots from which vorticity contours and a non-dimensional circulation were derived. The results should be of use in wing design where this secondary flow needs to be controlled.

We revisit our earlier study of targeted energy transfer (TET) mechanisms for aeroelastic instability suppression by employing time-domain nonlinear system identification based on the equivalence between analytical and empirical slow flows. Performing multiscale partitions of the dynamics directly on measured (or simulated) time series without any presumptions regarding the type and strength of the system nonlinearity, we derive nonlinear interaction models (NIMs) as sets of intrinsic modal oscillators (IMOs). The eigenfre-quencies of IMOs are characterised by the ‘fast’ dynamics of the problem and their forcing terms represent slowly-varying nonlinear modal interactions across the different time scales of the dynamics. We demonstrate that NIMs not only provide information on modal energy exchanges under nonlinear resonant interactions, but also directly dictate robustness behaviour of TET mechanisms for suppressing aeroelastic instabilities. Finally, we discuss the usefulness of NIMs in constructing frequency-energy plots that reveal global features of the dynamics to distinguish between different TET mechanisms and to study robustness of aeroelastic instability suppression.

The increasing environmental requirements in the air transport sector pose great challenges to the aviation industry and are key drivers for innovation. Besides various approaches for increasing the efficiency of conventional gas turbine engines, electric propulsion systems have moved into the focus of aviation research. The first electric concepts are already in service in general aviation. This study analyses the potentials of electric and turbo hybrid propulsion systems for commercial aviation. Its purpose is to compare various architectures of electrical powertrains with a conventional turboprop on a regional aircraft, similar to the ATR 72, on engine and flight mission levels. The considered architectures include a turbo-electric (power controlled and direct driven), hybrid-electric (serial and parallel) and a pure electric concept. Their system weights are determined using today’s technology assumptions. With the help of performance models and flight mission calculations the impact on fuel consumption, CO ${}_{2}$ emissions and aircraft performance is evaluated.

A systematic methodology for the thermodynamic optimisation of civil bypass engines (turbofan or advanced propulsors) is presented, which would be useful for designing air-breathing engines based on “clean-sheet analysis”. The process starts with establishing an optimum specific thrust for the engine based on an economic analysis (installation constraints, noise regulations etc. also need to be considered). The task of the optimisation process is then to find the combination of optimum values of fan pressure ratio, overall pressure ratio, bypass ratio and turbine entry temperature concurrently that maximises overall efficiency at the fixed specific thrust. This procedure is quite different from the usual single-variable parametric performance studies which do not give proper optimum values and may involve large excursion in the value of the specific thrust unacceptable for a particular mission. Additionally, several, simple and explicit, analytical relations are derived here from fundamental principles, which perform well against numerical optimisation performed by a specialist computer program employing iterative and advanced search techniques. The analytical relations accelerate the optimisation process and offer physical insight. Present numerical computations with real gas properties have established new concepts in turbofan optimisation (for example, the existence of an optimum bypass ratio and optimum turbine entry temperature). The question of optimum jet velocity has been addressed. An analytical expression for the optimum jet velocity at a given bypass ratio has been derived which performs well against numerical optimisation results.

In the coming century, the impact of air travel on the environment will become an increasingly powerful influence on aircraft design. Unless the impact per passenger kilometre can be reduced substantially relative to today’s levels, environmental factors will increasingly limit the expansion of air travel and the social benefits that it brings. The three main impacts are noise, air pollution around airports and changes to atmospheric composition and climate as a result of aircraft emissions at altitude. The lecture will review the work done within the Air Travel – greener by Design programme to assess the technological, design and operational possibilities for reducing these impacts. The main aeronautical disciplines all have something to contribute but it is in aerodynamics that the greatest opportunities appear to lie. If these opportunities are pursued, the aircraft in production in 2050 could be very different from those of 2005. It is for the aerodynamicists, supported by the structures and systems engineers and the materials scientists, to make the case for a radical leap.

An analysis is presented for the post-buckling behaviour of simply-supported, laminated cross-ply rectangular plates subjected to biaxial compression. The solution to von Kármán-type large deflection equations of the plate is expressed as a double sine series for the transverse deflection and a double series of clamped-clamped beam functions for the force function. All the boundary conditions, including those involving the normal bending moment at the edges, are satisfied exactly. The series solution is found to converge rapidly. Using only the first few terms in the series, numerical results for square graphite-epoxy unsymmetric laminates under uniaxial compression is presented graphically.