The Rayleigh-Ritz method is well known as an approximate method of determining the natural frequencies of a conservative system, using a constrained deflection form. On the other hand, if a general deflection form (i.e. an unconstrained form) is used, the method provides a theoretically exact solution. An unconstrained form may be obtained by expressing the deflection as an expansion in terms of a suitable set of orthogonal functions, and in selecting such a set, it is convenient to use the known normal modes of a suitably chosen “ basic system.” The given system, whose vibration properties are to be determined, can then be regarded as a “ modified system,” which is derived from the basic system by a variation of mass and elasticity. A similar procedure has been applied to systems with a finite number of degrees of freedom. In the present note the method is applied to simple non-uniform beams, and to beams with added masses and constraints. A concise general solution is obtained, and an iteration process of obtaining a numerical solution is described.

These notes are an attempt to examine what may be achieved in the way of performance, with existing materials and knowledge of aerodynamic engineering.

No claim is made for novelty, either in the data used or in the methods of working from such data to obtain the results arrived at.

Only the simplest engineering mathematics are employed so these results cannot claim academic accuracy, in fact they are most probably considerably inaccurate. But though inaccurate absolutely, the results should be accurate enough relatively for comparative purposes.

Full details of the methods employed are given in the various Appendices. This appears advisable, as it should make quite clear how the results are obtained and leaves it open for anyone to work out further examples by the same methods or to modify the methods themselves.

In recent years the need for high Reynolds number wind tunnel facilities has led to the development of the Cryo-genic Wind Tunnel. In this type of tunnel, the flow is cooled to extremely low temperatures, with the result that at constant Mach number the Reynolds number is greatly increased whilst the power required to drive the tunnel is reduced. The cryogenic tunnel incorporates a means of injecting liquid nitrogen into the free stream. The evaporation of this liquid cools the flow and some or all of the tunnel structure. Once the required low temperature has been reached a steady flow of liquid nitrogen into the tunnel and gaseous nitrogen out balances the heat input through the walls and from the fan and maintains constant pressure in the circuit. In addition to providing increased Reynolds numbers at reduced drive power, the cryogenic wind tunnel possesses numerous other advantages over its ambient temperature counterpart. For a detailed theory see Ref. 1.

Early in May 1785, Mr. Vincent Lunardi, famous for the first balloon ascent in England on 15th September 1784, announced that he would ascend again, in his new balloon, on 13th May, this time accompanied by his friend Mr. George Biggin and a lady.

For the occasion a stipple engraving (Fig. 1) was published, entitled “V. Lunardi, Esq., Mrs. Sage, G. Biggin Esq.”, showing these individuals in the balloon’s car. On the engraving, the date of publication is given as 13th May, the date fixed for the ascent, Mr. Bovi is named as the publisher, F. Bartolozzi as the engraver and Rigaud as the artist who had painted the picture from which the engraving had been made.

I would like to thank the directors of British Aircraft Corporation (Operating) Ltd for permission to give this lecture, but I must emphasise that the opinions expressed are my own. I would also like to acknowledge the considerable contribution that has been made by every Value Engineer in BAC to the pioneering work of introducing Value Engineering into our Corporation, and thank all those, both in BAC and in other aerospace companies in this country and in the United States, with whom I have discussed Value Engineering, and whose ideas have contributed to this paper.

Present aerospace development work is done in an environment which demands success. This has stimulated interest in methods of planning and controlling project development and costs more positively.

While some developers continue to hold the view that planning other than in the broadest terms is not compatible with high novelty development, the importance of new planning attitudes has been recognised. However, the very magnitude of a major aerospace project is such that the application of new planning and control procedures may in itself constitute a significant development programme, and it is not surprising that the industry has shown caution in introducing major changes of method.

The rapid growth of interest in fluid logic and control elements has refocused attention on the reattachment of two-dimensional jets to plane surfaces. Of particular interest is the size of the low-pressure bubble enclosed between the jet and the adjacent inclined plane, and the effect on this of fluid velocity and compressibility. Several full studies have been made of such flows, notably by Bourque and Newman, Sawyer and Olson, and the basic characteristics have been well established. Agreement has been reached that bubble length is independent of jet Reynolds number (above 104), but doubts remain as to the best method of measuring the bubble length and also as to the effect of compressibility on this measurement. In order to clear up some of these points for an investigation of compressible flow through control valves, some experimental tests have been carried out on the reattachment of air jets to a plane.

The purpose of this note is to present formulae, derived by stationary energy considerations, for the deflection of an arbitrary length of sandwich structure subjected to the three-point bend test, for comparison with experimental results.

The ‘universal’ Strouhal number, SB, which was derived by Bearman using the Kronauer vortex stability criterion is presented for two-dimensional rectangular-section prisms of depth to width ratio, d/h, from 1 to 5, for a flat plate with and without splitter plates, for a circular cylinder with splitter plates and for a circular cylinder with two blowing slots to control its wake width. A value of SB close to Bearman's value of 0·181 is obtained for the prisms of small d/h, for the plate without a splitter plate, for the cylinder with small splitter plates and for the cylinder for low blowing rates. For the other cases, however, SB is found to vary within the range 0·137 to 0·208 which is an indication that the general application of this concept to two-dimensional bluff bodies is superficial.

Before detailing the value of non-destructive testing in the aircraft industry, it seems best to explain aircraft structural design philosophies as they affect NDT.

Airworthiness and weight-saving are two over-riding factors in aircraft design. The important parameter from an economic standpoint is the weight. Fig. 1 shows the value of weight saving for a civil aircraft operator in £ per lb with typical values going up to £100 per lb per aircraft per year. (This figure shows the actual financial saving associated with the reduction in operating economics due to the lower weight.) But the vulnerability of an aeroplane in any failure case makes safety a paramount consideration. To save weight, design factors on aircraft are very low.

Data-driven methodologies based on the restoring force method have been developed over the past few decades for building predictive reduced-order models (ROMs) of nonlinear dynamical systems. These methodologies involve fitting a polynomial expansion of the restoring force in the dominant state variables to observed states of the system. ROMs obtained in this way are usually prone to errors and uncertainties due to the approximate nature of the polynomial expansion and experimental limitations. We develop in this article a stochastic methodology that endows these errors and uncertainties with a probabilistic structure in order to obtain a quantitative description of the proximity between the ROM and the system that it purports to represent. Specifically, we propose an entropy maximization procedure for constructing a multi-variate probability distribution for the coefficients of power-series expansions of restoring forces. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed framework.

The computer is seen as the greatest invention in history, in that it has a universality which transcends all other known inventions. It will ultimately be capable ot any process describable in terms ot an open or closed logical structure.

In a deterministic science such as aeronautics, it has clear capabilities in the solution of the equations governing fluid flow, structures, propulsion, navigation and so on. The speed and size of future computers, together with all sorts of new software techniques, will facilitate almost instantaneous solutions of any problems, within the next century.

There will be two major constraints on these developments which we can predict with confidence. The first is financial. The second is more subtle: there may develop sociological resistance to technological advances, especially to those wielding the power implicit in future generations of computers, and this carries important implications for scientists.

The pressure reading of a pitot tube in a supersonic flow corresponds to the position of the nose shock wave. Results of measurements of the shock stand-off distance are presented for three different streamwise Mach number gradients and for a uniform flow. These results are compared with existing theoretical values.

This paper applies existing information on solar storms to unmanned aviation; no new research data is presented. The purpose of this paper is to alert the unmanned aviation community to the potential hazards posed by solar storms, to familiarise it with the effects of solar storms and how to mitigate them, and to encourage research on solar storm effects on high altitude long endurance (HALE) aircraft and airship design and operations. As unmanned aircraft and airships move increasingly into high altitude (50,000+ft), endurance (24+ hr) roles, they will become vulnerable to the effects of space weather, specifically that of solar storms. Although solar storms are commonly associated with their impact on satellites, they affect the routing and timing of airline flights flying for six to eight hours at 30,000 to 40,000ft. Operating twice as high and with flight times twice as long (or longer) than those of airliners, HALE aircraft and airships occupy a middle zone of vulnerability, being more so than airliners but less so than satellites. A key difference however is that satellites are designed for space weather, whereas some current HALE vehicles are not. The paper concludes that unmanned HALE aircraft and airships can be one to three orders of magnitude more vulnerable to solar storms than a trans-Pacific airliner.

In their paper in the February 1967 Journal, Iyengar and Srinivasan have presented a solution to the problem of uniformly loaded clamped skew plates by employing characteristic functions for the modes of vibration of clamped-clamped beams. They compared their theoretical results with those obtained by Morley and Kennedy.

The writer has recently extended the 3-parameter solution by assuming a deflection function in the form:

Metal adhesives have been known to the Aircraft Industry for at least ten years, the Chrysler Cycle Weld process being among the earliest. Since then metal-to-metal bonding has been the subject of many papers, but no member of a firm of aircraft constructors is known to have lectured on the subject.

It is hoped, therefore, that this paper may prove a useful contribution to the workshop aspects of the method. The fundamentals of adhesion will be avoided and only brief reference will be made to the strengths of structures assembled by that means; those are matters for the physicist and aircraft designer.

In a recent study of the buckling of pin-ended struts of a certain light-alloy material the author found it necessary to use ball-end fittings which supported rigidly an appreciable length of the strut. For some of the struts—having slenderness ratios of the order of 20—the unsupported length was only about a quarter of the overall length between pinned-ends, (Fig. 1). The effect of rigid end-fittings can easily be taken into account in calculating the elastic buckling load of this system. The author expected to find this end effect important for shorter struts; however, this is not the case. In fact, buckling of the strut is governed largely by the flexibility of the unsupported length, and even large end fittings may not affect appreciably the buckling load.

Tests were made in the N.A.C.A. gust tunnel to determine the effectiveness of a long-period dynamically overbalanced flap in reducing aeroplane accelerations due to atmospheric gusts. For two gust shapes, one gust velocity, one forward velocity, and one wing loading, a series of flights was made with the flap locked and was then repeated with the flap free to operate. The records obtained were evaluated by routine methods.

The results indicate that the flap reduced the maximum acceleration increment 39 per cent, for a severe gust with a representative gust gradient distance of 8 chord lengths and that, for an extreme gust shape (a sharp-edge gust), the reduction was only 3 per cent. The results also indicate that the flap tended to reduce the longitudinal stability of the aeroplane. Computations made of the effectiveness and the action of the flap were in good agreement with the experimental results.