It is noted that the averaging technique of Beecham and Titchener, for obtaining approximate solutions to nonlinear, ordinary, differential equations, is not widely known or used. In its extended form, as given by Simpson and Ross it appears to offer a unified and useful approach to the solution of many dynamical and other problems. The present paper sets out to describe and discuss, through the medium of a collection of examples, the Beecham-Titchener-Simpson (BTS) method in an effort to encourage its more widespread use.

Propelled by the rapid advances in VLSI technology, supercomputers are now appearing with much larger real memory capacity than previously available. These new machines are expanding our ability to formulate very large-scale discrete models in order to discover non-linear dynamical flow behaviour. With a synergetic computational-analytical view point, we can begin to explore new and unexpected flow phenomena such as wave-like instabilities of vortices and even the onset of coherent large-scale turbulence brought about by vortex stretching.

‘Soon shall thy arm, Unconquer’d Steam! afar
Drag the slow barge, or drive the rapid car;
Or on wide-waving wings expanded bear
The flying-chariot through the fields of air.
— Fair crews triumphant, leaning from above,
Shall wave their fluttering kerchiefs as they move;
Or warrior-bands alarm the gaping crowd,
And armies shrink beneath the shadowy cloud.’

In this paper a direct digital control law algorithm is proposed which in addition to providing tight non-interacting tracking behaviour and excellent disturbance-rejection characteristics, provides for the compensation of finite-time delays in implementation. The control-law algorithm is defined and system stability is proved in the case of multi-input multi-output linear systems. The theory is synthetic and leads directly to the determination of the appropriate controller matrices.

The theory is illustrated by the presentation of simulation results in which the aircraft is represented by an analogue computer and the digital control system is implemented on a microprocessor. In the simulation study the controller is required to effect fuselage pitch pointing and vertical translation manoeuvres for the analogue computer representation of the YF-16 aircraft. It is shown that tight non-interacting control is achievable even when the control implemented is delayed by 0·1 seconds.

For the computer simulation of bodies moving through real fluids input data about the aerodynamic and inertial forces and moments developed on them are required. It has long been known that under appropriate conditions the apparent masses of the body can play an important role in the determination of dynamic characteristics and this is certainly the case with parachute systems. In the past, because of inadequate experimental investigations, not all of the implications of apparent mass for this system have been fully appreciated. The current objective is therefore, in the light of experiments conducted on the measurement of apparent masses for some parachute canopies, to derive the relevant equations of motion for the parachute and store system and thus to determine the effects of various parameters on the dynamic characteristics of fully-deployed parachutes. In this system the store has been assumed to be rigidly connected to the canopy.

The estimation of the relative orders of the coefficients in the linear differential equations of longitudinal small perturbation of aircraft is used to analyse the classical simplified theory for the short- and long-period modes by the singular perturbation methods. The leading terms of the asymptotic expansions give the eigenvalues for short- and long-period modes with fairly good accuracy, except that the damping part of the eigenvalue for the long-period mode has relative error of the order of 10%. These approximate eigenvalues are improved by the method of strained co-ordinates which accounts for most of the differences. The dynamic response due to initial disturbances of velocity, angle of attack, and angle of pitch are also derived.

This paper presents experimental data highlighting the effects of a forward facing aerodynamic spike on the pitch stability of a blunted cone in hypersonic flow. Spike length and angle of attack variations on stability derivatives are described. Suitable application of the inviscid embedded Newtonian pitch stability prediction technique shows how the influence of spike aerodynamics may be successfully modelled. The paper extends the knowledge of aerodynamic spike flow effects, which have to date concentrated on aerodynamic drag reduction qualities at zero degrees angle of attack.

Research at RSRE has revealed significant problems in the use of commercial microprocessors in safety critical equipment. The difficulties arise from the imprecise documentation of the instruction sets by the microprocessor manufacturers and changes in internal design and external functionality during the years a popular device is marketed. To meet certain defence needs, RSRE is conducting research on formal methods of design and implementation of VLSI chips which provide simple processing capability and can be proved to be functionally correct. The first product of this research is a new 32-bit microprocessor architecture, called VIPER, which is described in outline in this paper. Although the primary application of such high integrity devices is in the defence field it is believed that they would be of great value in civil aviation, both in fast control loops in aircraft and in the control of critical DVOR/ DME, ILS and MLS transmitters on the ground.

An experimental study has been made of the conditions necessary to produce transition in a swept attachment-line boundary layer which is subjected to disturbances from trip wires of various sizes. The boundary layer considered is that formed on a long, untwisted, tapered wing which has been tested in both the backward swept and forward swept configurations. Results from these tests are compared with previous work on an untapered model. Some important similarities and some puzzling differences have been found. Finally consideration is given to the practical implications of this work. It is suggested that a forward swept wing may be capable of supporting a laminar attachment-line flow at a much higher free-stream Reynolds number than a corresponding swept-back wing.

Since it is not assumed a priorito be constant, entropy can vary along streamlines in the numerical solution of the Euler equations, depending upon its accuracy, even if the flow is isentropic. The level of this spurious entropy (or equivalently loss in total pressure) produced in the solution has become a common measure for the accuracy of the solution. It was used in a recent exercise by the AGARD Working Group 07 as one of the primary criteria to judge the most accurate solutions of the Euler equations for a variety of different test problems. Of the four possible sources of this error: mesh spacing, convective difference scheme, artificial viscosity model, and boundary conditions, the latter two are found to contribute the most. The steps taken to limit the errors coming from each of these four areas are described in detail in the context of two AGARD test cases: NACA 0012 M∞, = 0·85 α= 1 deg, and NLR 7301 M∞ = 0·721 α=-0·194 deg. An accurate shock-free supercritical solution is presented for the latter case.

The method of images is used to calculate the analytical solution for an inviscid incompressible flow past four arbitrary circles which are then conformally mapped onto aerofoil sections. The analytical solution of the corresponding flow past the system of aerofoils is obtained and the pressure distributions about a particular three-element and a particular fourelement aerofoil are presented. These results are intended to be used to assess the accuracy of numerical methods.

It is shown, fairly rigorously, that large aerospace projects, with typical periods of 15 years to break even, are unlikely to provide a commercial rate of return on a ‘risk’ investment. However, they can generate enough surplus to meet an alternative criterion, the ‘self-financing ratio’, which emphasises the contribution made by the Project to the future self-financing capability of the company. Until this blessed state is achieved, the industry needs ‘cheap money’ whose main source can only be the taxpayer. The role of the taxpayer as investor is examined with the help of an elementary econometric model. A form of ‘Prospectus to the Taxpayer’ is developed which summarises the quantifiable benefits to the national economy arising from the launch of a project. The same methods are also applied to the formulation of a ‘Home-Purchase Discount’, intended as an aid to government procurement decisions. The concluding remarks emphasise that the paper is relevant primarily to the ‘large scale high R&D sector’ of industry, of which aerospace is a prominent component.

Finally, the views expressed in this paper are my own and emphatically do not reflect those of the Company I have the honour to serve in other fields

The separation of boundary-layer flow from a wing or in a diffuser usually defines the limit of efficient operation, so it is important that the onset and development of separated flow can be predicted. The calculation of the interaction of the shear layout close to an aerofoil with the external inviscid flow has offered an attractive alternative to solving the Reynoldsaveraged Navier Stokes equations for attached flow: the interaction method is much faster. In this paper it is shown how the interaction approach can be extended for use with separated flows and the development of a practical method is described. The calculation of the shear layer through the singularity at separation is accomplished by using an inverse mode. Beyond separation the empirical definition of a new family of velocity profiles allows an integral calculation of the shear layer to proceed up to the reattachment. The solutions for the shear layer close to the aerofoil are matched to the external inviscid flow by a ‘semi-inverse’ method. A careful examination of the stability of this method leads to rapid convergence for separated and attached flows. As an illustration the stall and post stall behaviour of a twodimensional aerofoil is predicted and compared with experimental results.

By introducing experimentally-obtained apparent mass components into the relevant equations of motion, performance characteristics of descending parachutes have been obtained which so resemble those observed as to give an appropriate basis for performance prediction. The effects on pitching oscillations caused by certain changes in system physical parameters; the size of the parachute canopy, the length of the rigging lines and the store mass, have all been considered as well as the effect of parachute altitude. For good stability in pitch the significant ratio of physical parameters is that of store mass to effective canopy mass, inclusive of apparent mass.

Tonight, once again, we honour the memory of Frederick William Lanchester, one of the great pioneers of modern engineering, born in 1868 died in 1946. We keep his memory alive by exploring how his ideas and concepts have flowered into maturity, and by reminding ourselves that his example, philosophy and strength of purpose are still relevant in today’s world. I suppose each of us reacts individually to the life and work of a great man.

A computational method is presented for solving numerically the three dimensional Euler equations for transonic flow around practical aircraft forebodies. The Euler solver is pseudo-time dependent, split and cast in finite volume form. Shock waves are captured crisply without the need for additional smoothing by means of an operator-switching facility which more accurately reflects the direction of propagation of signals.

The method is illustrated by examples of computed external, axisymmetric flows and some, simulated, realistic aircraft fore-bodies. The computational meshes employed in the three dimensional cases are essentially of cylindrical polar, flow conforming, type and relatively coarse. Closer attention to the mesh generation is expected to refine the results presented here. The method is versatile, robust, and holds promise for treating complex three dimensional geometries within economically viable run times.

The experimentally observed changes in the location of boundary layer separation on the cylindrical afterbody of a tangent-ogive-cylinder, placed at incidence in a uniform flow, are related to the phenomenon of laminar-turbulent transition. Existing knowledge of the transition mechanisms which operate in general, three-dimensional; boundary layers, is described and simple prediction criteria are derived for this configuration. These criteria are compared with the currently available empirical methods for the prediction of critical Reynolds numbers for such flows. It is demonstrated that the methods which have been published to date are incomplete and the accompanying analyses are based upon superficial and erroneous physical arguments. The implications of boundary layer transition on the normal forces generated by a cylindrical afterbody are also discussed. Finally, the possibility of using transition fixing to establish ‘high Reynolds number’ separated flows in ‘low Reynolds number’ wind-tunnel facilities is briefly considered.

In the flow over high-lift aerofoils there is a strong interaction between the wake from one element and the boundary layer on another element immediately downstream. A number of experimental investigation of these types of flow have been made but these studies do not allow the effects associated with the various parameters of the aerofoil to be seen easily. This paper presents the results of extensive measurements of mean and fluctuating quantities made in merging layers in zero and adverse pressure gradients downstream of aerofoils of various shapes. A general description of the emerging process is given and the effects of wake characteristics and pressure gradient are considered. The paper also contains a discussion of the modelling of the Reynolds shear stress in the merging layer.