The many methods by which Pontryagin's Maximum Principle is applied in optimal control problems can be divided into two groups, termed direct and indirect. The indirect methods use the conditions required for mathematical optimality as the starting point and attempt to satisfy the boundary conditions. The direct methods on the other hand satisfy the equations of motion and boundary conditions and then attempt to improve the performance index. It has been reported that the direct methods, while normally converging from very bad initial assumptions, have the inherent disadvantage of very slow convergence in the neighbourhood of the optimal solution and, so, complicated second order methods have recently been devised.

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.

This paper presents an open framework, through which, conventional general purpose aerial munitions can be converted into smart munitions. The retrofit consists of a smart adaptation kit (SAK) having a dedicated Guidance and Control Module (GCM). The adaptation kit along with the GCM ensures that the SAK glide optimally towards the designated target. To reduce cost, the number of control surfaces of the SAK has been kept to a bare minimum, which resulted in an under actuated system. The methodology proposed utilises the theory of gain-scheduled control and leads to an efficient procedure for the design of the controllers, which accurately track reference trajectories defined in an inertial reference frame. The paper illustrates the application of this procedure to the design of stabilisation and tracking controller for the SAK. The design phase is summarised, and the performance of the resulting controllers is assessed in simulation using dynamic model of the vehicle. Simulation results show that apart from improved circular error probable (CEP) of hitting the target, munition ballistic range has also significantly increased with the proposed modification.

Two alternative presentations are given of Patel’s Preston tube calibration. In the first, Δp/τw is tabulated as a function of Δpd2/ρν2; in the second, cf is plotted as a function of Δp/½ρU2 and Ud/ν, so that values of cf, can be read off directly.

A discrete-vortex representation of the wake of a circular cylinder, in which vortices are convected in a potential-flow calculation and maintain their identities unless they approach one another or a surface closely, predicts many of the unsteady flow features and is computationally more efficient than other schemes. The mean rate of shedding of vorticity is adjusted to be compatible with experiments at a high subcritical Reynolds number of 3 × 104 and the model gives reasonable predictions of separation, drag, lift, Strouhal number and vorticity loss in the formation region. The method is extended to accommodate a second cylinder and many of the surprising features which have been observed experimentally with two cylinders in a side-by-side arrangement are reproduced.

Effusion cooling consists in forcing a gas under pressure through a porous material thereby absorbing heat from the material and forming a heat insulating layer on the exposed surface. The internal heat transfer between the porous material and coolant is considered and the heat transfer coefficient obtained from experiment. An approximate analysis for the heat insulating effect based on a heat balance method is derived in detail and applied to experiments with porous plugs set into the side of a duct carrying hot gases, and to porcras cylinders swept by hot gases. It has been found that this analysis applies reasonably accurately to the results of these experiments and of most of the published data. The manufacture of porous materials is discussed briefly and a representative list of commercially available materials is included. The application of effusion and sweat cooling to the blading and combustion chamber linings for gas turbines, rocket motors and the outside skin of flying vehicles is considered.

One of today’s most propitious immersive technologies is virtual reality (VR). This term is colloquially associated with headsets that transport users to a bespoke, built-for-purpose immersive 3D virtual environment. It has given rise to the field of immersive analytics—a new field of research that aims to use immersive technologies for enhancing and empowering data analytics. However, in developing such a new set of tools, one has to ask whether the move from standard hardware setup to a fully immersive 3D environment is justified—both in terms of efficiency and development costs. To this end, in this paper, we present AeroVR—an immersive aerospace design environment with the objective of aiding the component aerodynamic design process by interactively visualizing performance and geometry. We decompose the design of such an environment into function structures, identify the primary and secondary tasks, present an implementation of the system, and verify the interface in terms of usability and expressiveness. We deploy AeroVR on a prototypical design study of a compressor blade for an engine.

Using Rayleigh's principle, the natural frequencies of thin isotropic rhombic plates, with three possible combinations of boundary conditions obtained by combining clamped-clamped and clamped-supported edge conditions, are determined in Part I of this paper. To introduce constant limits of integration, non-orthogonal co-ordinate systems are used and the wave shape for the vibrating plate is approximated by using normal functions representing mode shapes of corresponding bars. To estimate the accuracy of these eigenvalues, Kato's theorem is used and the lower bounds for the natural frequencies are determined in Part II of the paper. It is also shown that normal beam functions are not generally suitable for the determination of eigenfrequencies of skew plates with large skew angles.

Microwaves are a form of electromagnetic radiation commonly used for telecommunications, navigation and food processing. More recently microwave technologies have found applications in fibre-reinforced polymer composites, which are increasingly used in aircraft structures. Microwave energy can be applied with low power (up to milliwatts) for non-destructive testing and high power (up to kilowatts) for heating/curing purposes. The state-of-the-art applications at high power include curing, three-dimensional (3D) printing, joining and recycling, whereas low-power microwave techniques can provide quality checks, strain sensing and damage inspection. Low-power microwave testing has the advantage of being non-contact, there is no need for surface transducers or couplants, it is operator friendly and relatively inexpensive; high-power microwave energy can offer volumetric heating, reduced processing time and energy saving with no ionising hazards. In this paper the recent research progress is reviewed, identifying achievements and challenges. First, the critical electromagnetic properties of composites that are closely related to the heating and sensing performance are discussed. Then, representative case studies are presented. Finally, the trends are outlined, including intelligent/automated inspection and solid-state heating.

A method of obtaining the load distribution on thin rectangular wings in non-stationary incompressible flow is presented, with particular reference to the problem of gust-induced loading. The method utilises solutions to a Fourier transform of the downwash integral equation, enabling the problem to be expressed in the form of a set of dual integral equations having a series solution. Some values of the overall lift coefficient are computed and compared with values of lift coefficient obtained by collocation methods. The method is easily extendable to subsonic compressible flows.

In this study, a new aero-propulsive model (APM) was derived from the flight manual data of a transport aircraft using Genetic Algorithms (GAs) to perform accurate trajectory predictions. This new GA-based APM provided several improvements to the existing models. The use of GAs enhanced the accuracy of both propulsive and aerodynamic modelling. The effect of compressible drag rise above the critical Mach number, which was not included in previous models, was considered along with the effects of compressibility and profile camber in the aerodynamic model. Consideration of the thrust dependency with respect to Mach number and the altitude in the propulsive model expression was observed to be a more practical approach. The proposed GA model successfully predicted the trajectory for the descent phase, as well, which was not possible in previous models. Close agreement was observed when comparing the time to climb and time to descent values obtained from the model with the flight manual data.

The Technology Sub-Group of Air Travel – Greener by Design was instituted at the first full meeting of the GBD community in March 2000. Its first period of intense activity was from the summer of 2000 to the spring of 2001, culminating in the publication of its report The Technology Challenge in July 2001 at the first Air Travel – Greener by Design Conference at the Royal Aeronautical Society.

In the period that followed, the contents of the report were further disseminated by presentations at conferences and publication of the report in The Aeronautical Journal but there was no substantial activity by the Sub-Group as such. In July 2003, a workshop on ‘The Effect of Aviation on the Atmosphere’, was held at St Catherine’s College, Cambridge. This was planned jointly by members of the Sub-Group and of the Centre for Atmospheric Science in the Department of Chemistry at Cambridge and was jointly funded by GBD and the EC project SCENIC. The organisation of events on the day and the collating and editing of the workshop report was done by Dr Helen Rogers of the Centre for Atmospheric Science. The workshop was attended by a broad cross section from the manufacturing and operating industries, government and academia and its report is a valuable summary of current understanding in 2003.

Optimisation of complex systems frequently requires evaluating a computationally expensive high-fidelity function to estimate a system metric of interest. Although design sensitivities may be available through either direct or adjoint methods, the use of formal optimisation methods may remain too costly. Incorporating low-fidelity performance estimates can substantially reduce the cost of the high-fidelity optimisation. In this paper we present a provably convergent multifidelity optimisation method that uses Cokriging Bayesian model calibration and first-order consistent trust regions. The technique is compared with a single-fidelity sequential quadratic programming method and a conventional first-order trust-region method on both a two-dimensional structural optimisation and an aerofoil design problem. In both problems adjoint formulations are used to provide inexpensive sensitivity information.

In this note, the experimental results of wind-tunnel measurements of lift coefficient and lift-curve slope for aerofoil NACA 0012 obtained from the VTI-Institute Zarkovo, are presented. The results were obtained from tests and integrations of surface static-pressure data over a model of the NACA 0012 aerofoil section. The data were obtained for a free-stream Mach number range of 0·25-0·8 and a chord Reynolds number range of 2-25MRe. The essential results of these measurements along with the results from other authors are presented and evaluated. The principal factors which influence the accuracy of two-dimensional wind-tunnel test results are analysed. The influences of Reynolds number, Mach number and wall interference with reference to solid and flow blockage as well as the influence of side-wall boundary-layer control are analysed. Interesting results brought to light the Reynolds number effects of the test model versus Reynolds number effects of the facility in subsonic and transonic flow as well as the effects of the side-wall boundary-layer control and wall interference.

The problem of the buckling of flat oblique plates (i.e. in the shape of parallelograms) with all edges clamped under a uniform system of stress is considered. An energy method of calculating the critical stresses is developed and applied to the particular case of a clamped oblique plate under uniform compression parallel to two of the sides. Numerical values for the buckling stress coefficient are obtained for plates having acute angles of 60° and 45°, and side ratios varying between 3/5 and 5/3.

The influence of spanwise correlation of fluctuating pressures due to vortex shedding on the total oscillatory loading of a long bluff cylinder in cross-flow is considered. Experimentally determined pressure correlation lengths on a stationary and vibrating cylinder of square cross section are then combined with previously obtained chordwise pressure distributions to demonstrate the amplification of the oscillatory lift on a long bluff cylinder during cross-flow vibrations.

The existing data relating to stresses round pins in holes are reviewed and co-ordinated.

The first part of the paper deals with pins of which the diameter is less than half the plate width and which are no better than a push fit in the hole; the second section deals with larger pins; and the third section deals with interference fit of the smaller pins. The theoretical background is sketched in two appendices, and the results of three series of photoelastic measurements of the effects of clearance of the pin in the hole are described.

Many situations arise in which aerospace structures are subjected to high frequency excitation, in the sense that the wavelength of the induced dynamic response is much shorter than the overall dimensions of the structure. The application of the conventional finite element method to this type of problem faces two difficulties: (i) the short wavelength of the structural deformation requires the use of many elements, which renders the method computationally expensive or even impracticable, and (ii) the response of the structure at high frequencies can be very sensitive to structural detail, and thus response predictions for an ‘ideal’ structure may differ significantly from the performance of the actual system. For a number of years research effort has been directed towards the development of alternative analysis methods for high frequency vibrations, and recent developments in this area are reviewed in the present paper. The methods considered are: (i) hierarchical versions of the finite element method, (ii) the dynamic stiffness method, (iii)periodic structure theory, (iv)statistical energy analysis and (v) wave intensity analysis.

Topology optimisation is a useful tool for the design of aircraft structures. This work details how the new moving iso-surface threshold (MIST) topology optimisation method works and how it can be applied to aircraft structural design. This method has been coupled with commercial finite element analysis software in a simple manner without requiring the modification of the commercial software source code. In this way the user is able to take advantage of the finite element analysis tools such as automatic mesh generation and efficient solving. The extension of the method to 3D designs is also presented. The topology results of a 2D leading-edge rib for stiffness, stress and morphing objectives and a 3D wing skin stringer for stress design demonstrate the functionality of this method.

The object of this paper is to set down an overall picture of the practical aspects of compressor blade vibration. In doing so it is inevitable that a certain content is effectively a repeat of other people's contributions to the subject. The authors make no apology for this and offer the paper as a "state of the art" as practised at Bristol Siddeley Engines Ltd. In bringing together the many relevant issues of this problem, it is hoped that a useful presentation is obtained.

There is little hesitation in indicating the most obvious and important practical aspect of blade vibration as that of the inherent danger of blade failure and it is known that the axial flow compressor is susceptible to complete failure caused by the fatigue of one blade.

The multi-stage axial flow compressor is a highly complex aerodynamic machine with, its early and late stages required to operate over wide ranges of incidence and Mach number conditions. To some extent, of course, use of variable geometry can reduce this to less taxing proportions. The aerodynamic environment of front stages has broad boundaries somewhat wider than those relating to rear stages, while middle blade rows generally operate under sensibly constant conditions. This diminishing “severity” of operation, front, rear to middle stage blading is not unrelated to the incidence of blade vibration problems which shows a similar pattern.