In addition to direct solar radiation, this paper includes the effect of direct earth radiation, its albedo and shadow on the attitude dynamics of gravity orientated systems, thus extending the analysis of Part I down to the earth's effective atmosphere. The importance of these radiations was indicated by a preliminary force analysis, which revealed that they can exert a force comparable to that of direct solar radiation for close earth satellites. Thus, the need for a rigorous investigation including the effect of earth radiations on satellite attitude dynamics is evident.

Earth radiation forces were obtained in integral form by Clancy and Mitchell using elementary radiation principles. However, in a test on an IBM-7044 digital computer, it was found that the time required to evaluate these integrals renders a study of satellite attitude dynamics virtually impossible.

In an analysis by the matrix force method of a structure containing thin tubes of open cross-section, it is commonly assumed that the torsional stiffness of such members may be taken into account by considering the St. Venant shear stresses only. This effectively introduces the assumption that the cross-section of an open tube is able to warp freely, whereas in practice the warping may be constrained by the surrounding structure.

In this note a method is presented which allows such warping constraint effects to be taken into account in a finite element analysis using the Force Method. Because of the assumption of linear variation of direct stress along the element the full flexibility matrix does not have to be used, which may be an advantage in certain cases. The “exact”, but more complex, flexibility matrix has been derived and will be presented in a later note.

My paper is concerned with Operational Assessment on Air-to-Air, Air-to-Ground and Naval Surface-to-Air Guided Weapons.

I will start by describing the strategy and tactics for the use of these weapons to provide the military environment against which operational assessment is carried out. I will then say something of the methods we use of measuring the effectiveness of weapon systems by taking a number of examples and illustrating some of the different approaches we have used in the past.

In a Symposium held here in November 1970 entitled “Compensation for Death and Injury in International Air Transport” we heard of the latest ICAO proposals towards resolving such liability problems as far as the airlines were concerned and there was much informed debate on the merit (or otherwise) of limiting claims arising out of an aircraft accident. It was unfortunate, but understandable, that that symposium could not be combined with today’s discussion since the basic problems are much the same. As I sought to point out on that occasion, there could be little advantage in protecting the airlines’ front door, by limiting the amount of damages available to a plaintiff, if the airlines back door was left exposed—due to the vulnerability of the airlines to a cross claim for indemnity or otherwise from a manufacturer who, more likely than not, would be a joint defendant with the airline in the same or parallel proceedings arising out of the same aviation accident. This should mean, at the very least, close collaboration between the airlines and manufacturers and, more preferably, some form of shared protection which they may create together or which may be granted to them by Government action, national or international.

The von Mises yield criterion for sheet material under conditions of plane stress is given by

where σ1, σ2 are the principal stresses in the plane of the sheet and σy is the yield stress under uniaxial tension. If equation (1) is expressed in terms of elastic strains by virtue of the relations:

where v=Poisson's ratio and E=Young's modulus, it is found that when

the term in ∊1∊2 vanishes and the criterion for the onset of yield simplifies to

Now v* is very close to that of most materials of structural interest.

I had thought that perhaps, one time I could appear here and say something without being contentious but I must immediately start off with a significant argument. I think that as a plantiff's lawyer in the United States I am one of a large number of responsible members of the Bar, and I say this in all innocence, doing a responsible job which I am sorry to say is frequently misunderstood here. I do not think we set out to bankrupt the British or American aviation industries. I do not think we set out to make fortunes for ourselves, or our clients. I think sincerely, that the objectives of the typical plaintiff's lawyer is to get reasonable redress for the poor victims of tragic accidents.

The need to understand the mechanism of generation and to be able to predict the noise of aircraft has increased enormously in the present decade. The questions which the aircraft designer now poses to the noise engineer are much more difficult to answer than was the case in 1964 when rotorcraft noise was discussed by this Section. For example in the case of conventional transport aircraft at the beginning of this decade it was only necessary to show that on take off the peak noise did not exceed 110 PNdB at a predetermined monitoring point at certain airfields. With the advent of noise certification it is now necessary to know the complete noise time history of the aircraft for points under the take off path, at the side and on the approach before the aircraft flies or the engine is made. The increased emphasis on noise research and the resulting developments in the theory and practice is not surprising.

The problem of obtaining proper flow spreading together with useful pressure recovery across rapidly expanding diffusers is of considerable practical importance. Many different approaches to this end have been reported in literature, e.g. vortex generators, screens or baffles, surface roughness, corrugations, etc., apart from the use of direct boundary-layer control. These methods have the common aim of preventing separation from the walls of the diffuser. With increasing expansion angle and area-ratio, however, the effectiveness of these methods either breaks down or is obtained at a high cost of pressure recovery.

The purpose of this note is to outline the basic physical features of parametric oscillation or instability and to show how situations might arise in practice in aircraft structures in which these effects would be significant. In most situations, the appearance of parametric oscillations will be the exception rather than the rule because of the relatively stringent conditions for its existence as a substantial component of the response. Nevertheless it is felt that the dynamicist should be aware of the phenomenon and should have some knowledge of its nature both as an aid to its recognition when it does appear and as a guide to the sort of situations in which it might be expected.

At BAC Filton the use of computers in missile work began early in the 1950s, much as elsewhere no doubt, by the company manufacturing its own analogue machines. The utilisation of computers was brought about by the need to develop the theoretical approach of design beyond the stage of hand computed calculations. Linear calculations could be long and tedious, and although ingenious exposure of the basic principles of missiles were often very instructive, they remained too simple to give complete reassurance.

As the development of missiles proceeded, the realisation of the complexity and extent of the non-linearities became more evident, casting doubt on the likely success of the missiles under design and manufacture. Typically with Bloodhound there was the fear that a twist/steer missile would not work, most missiles of the day being tail controlled cartesians. Would one be able to keep the body movements down to an acceptable minimum for the sake of aberration or ramjet extinction? Just what were the cross coupling effects from pitch and roll into yaw? Later, when what one might call the purely mechanical reliability aspects of trials were over, the need to understand the interaction of the various phenomena of missile flight began to dominate design thought.

Taxiing induced vibrations in large aircraft due to runway unevenness have been recognised as a significant factor in causing metal fatigue damage and dynamic stressing in airframes, as well as crew and passenger discomfort. The purpose of this paper is to develop a method of analysing random vibrations of a flexible aircraft, taking account of non-linearities in the oleo-pneumatic undercarriage in the form of orifice damping and Coulomb friction. The analysis assumes that the random input to both main undercarriage legs is identical, therefore it only considers symmetrical wing modes in the general deformation of the airframe.

The problem of aircraft noise has been touched on by a number of today's speakers, but I wonder how much it is appreciated that probably the biggest single interface problem before the aviation industry today is that of environmental pollution.

The dilemma which every Minister responsible for civil aviation has to face is how to strike a right balance between, on the one hand, economic and operational considerations and, on the other, the protection of the public from excessive noise. Successive Ministers have indicated very clearly to the Department that they favoured paying a substantial price, if required, for the preservation of amenity.

In a recent note, Allen has investigated the use of Preston tubes and Clauser charts for determining the skin friction in supersonic, boundary-layer flows. He concluded that the Preston tube was best used in conjunction with the law of the wall of Fenter and Stalmach but that the Baronti and Libby wall law was most suitable for determining local skin friction from velocity profiles; both methods are complex and do not permit the direct use of Clauser charts. The present note presents a simple transformation which permits incompressible Clauser charts to be used for the evaluation of skin friction in supersonic flows; the method is applicable to both adiabatic and nonadiabatic situations. Some conclusions, based on experimental experience, are drawn regarding the determination of skin friction by sub-layer methods.

At the present time, the only established method of metering a pulsating fluid flow involves the installation of damping devices in the system between the source of pulsation and the flow meter to ensure that the flow through the meter is essentially steady. Such devices may comprise a combination of frictional and volumetric damping and the method by which the required degree of damping is determined makes use of the Hodgson criterion. In many systems, it is undesirable (or, at least, inconvenient) to have to incorporate this damping and, therefore, the more direct approach, involving the metering of flow which is actually pulsating, is of considerable practical interest.

In the present note, the various factors affecting the metering errors in pulsating flow are discussed in relation to the results of an experimental investigation into the pulsating flow of air through a number of standard orifice configurations.

Considerable research effort has been devoted to the experimental and theoretical study of turbulent boundary layers on flat plates. However, relatively little research has been done on turbulent boundary layers in the presence of transverse curvature. In this paper transverse curvature denotes curvature in a plane normal to the flow direction as shown in Fig. 1. In particular, flow along the outside of cylinders is considered.

In most of the experimental and theoretical investigations of the cylindrical boundary layers (see for example references 1 to 4) the effect of transverse curvature on the velocity profile, especially on the power law, was not considered. Exceptions to the above statement are Rao's inference on the velocity profile and Bonsignore's prediction of change in the index of the power law.

The application of matrix displacement methods to elastic problems leads to an array of simultaneous equations, of the form:

in which K is non-singular. This, when inverted, enables the component deflections u to be determined for any specified loading f. The deformed shape of the system is thus obtained in terms of displacement of the nodes and the latter are used to derive the stress within each element. The stress solution thus lacks precision, since it is not clear as to what point within the element the calculated stress refers. There will be a number of such elements connected to any given node and generally, the computed stress is different within each.

The stress analysis of an axisymmetrical body under the influence of a field of centrifugal body force is of considerable importance to the design of rotating machinery. The classical problem of the rotating disc of uniform thickness was considered by Maxwell as long ago as 1850. For this, the simplifying assumption that the stresses are functions of the distance from the centre only, with no change across the thickness, was made. Since then, the same basic analysis has been extended to discs of conical and hyperbolical cross-section profile, with or without a central hole, references to which may be found in a number of text books. The analysis of a disc with an elliptical cross-section was published by Chree in 1895. The solution for a disc of constant thickness has been refined to allow stress variation across the thickness. Although these solutions, in common with many analytical solutions in the theory of elasticity, do not satisfy all the boundary conditions exactly, they serve as very good approximations in practice.

Practical problems often arise in which the aerodynamic loadings on wings and fins, due to nearby free vortices, are required. For example, aerodynamic loads on helicopter blades are affected by the tip vortices which are continuously being shed and which lie beneath the rotor plane. And vortices shed from the nose of an aircraft fuselage can induce significant side loads on a fin.

The estimation of the aerodynamic load distribution on a moving wing in the neighbourhood of a free vortex (whose axis is primarily in the free stream direction) is an interesting problem which, as far as the author is aware, has not been discussed previously in the literature. Standard techniques for conventional linearised wing theory cannot be applied directly to this problem because the trailing vorticity shed from the wing trailing edge is affected by the flow field of the free vortex and so the mathematical application of the Kutta trailing edge condition is more complex.