The 899th Lecture to be given before the Royal Aeronautical Society was held on 11th February 1954 at the Institution of Mechanical Engineers, Storey's Gate, London, S.W.I. Mr. G. R. Edwards, C.B.E., F.R.Ae.S., Vice-President of the Society, presided. Introducing the Lecturer, Dr. D. Williams, M.I.Mech.E., F.R.Ae.S., Mr. Edwards said that Dr. Williams was really too well known to need any introduction; his activities had been devoted in recent years to structural problems as applied to aeroplanes. Without reciting his attainments in detail, the job he had tackled in recent years at the Royal Aircraft Establishment and about which he had written papers, covered such subjects as vibration, wing flutter, sandwich construction, the effect of blast on aeroplanes, energy theorems, fatigue, dynamic loading by gusts and landing impacts, water-borne runways and nose-wheel shimmy, a variety of subjects one or all of which had caused most of them a great deal of anguish at one time or another.

The problem of deducing resonance modes of vibration of an aircraft in free space is a concomitant of flutter calculations if the number of degrees of freedom used is to be small. When the structure is complex in that it involves wings, fuselage and tailplane, each of which possesses infinitely many normal modes, it becomes apparent that the number of point masses which must be considered, in constructing a dynamical equivalent to give a sufficient coverage of the frequency range in which flutter is likely, is very large. For example, it may be necessary to use four rods per wing and per tailplane and four point masses on the fuselage. This would involve 8 + 8 + 4 degrees of freedom, and if the usual technique of characteristic roots is used it would be necessary to consider a characteristic root matrix of order 20 × 20.

Aircraft engineering has been described as “ordinary engineering made more difficult.” Probably most of you will agree that our difficulties are often greater than those that confront other branches of the engineering profession, and that the chief source of them is our inability to forecast with entire confidence what air will do under any given circumstances. Our position in this matter is much better than it was, for instance, at the end of the war. During the last thirteen years we have seen the theories associated with the name of Professor Prandtl receive general acceptance, with a profound effect upon our attitude towards some of the most important practical problems of air-flow with which we have to deal, namely, those associated with the production of lift. The boundary layer, then little more than a scientific curiosity, has become a matter of common concern. It achieved a striking practical success in the rationalisation of the international tests of airship models, which led to a marked advance in our attitude towards the whole problem of scale effect. But in many respects we are still greatly hampered. In so far as there has been any advance in the pure hydrodynamical theory of the flow of viscous fluids, it is hardly too much to say that its practical effect has been negligible. What then are we to do?

Increasing interest has been shown recently in the measurement and interpretation of post-yield strains. Early investigators determined the nature and magnitude of such strains by observing the distortion of a grid of fine lines inscribed on the unstrained metal. A development of this method involved the use of a photographically deposited grid.

In the present instance the initial requirement (August 1948) was for the measurement against time of strains of the order of 4 per cent. occurring as “ fast transients.”

As the wire resistance strain gauge element was well established, it was natural to consider its extension to post-yield measurements, and it later became apparent that this had already been done by Swainger.

The normal functions of beam vibration may be used in series to solve statical problems of beam flexure and the recent appearance of tables of these functions has rendered this method practicable. An outline is given of the procedure.

The simple equation of free flexural vibration of beams is

1

where v is the displacement, EI the flexural rigidity andAp the mass per unit length. The separation of variables and the application of appropriate boundary conditions at the ends x = 0 and x = l, gives the following normal functions ϕ(x).

The regular operating heights of aircraft, both civil and military, are continually increasing until now regular flights within the stratosphere are planned. There is, therefore, much practical interest in the meteorological conditions to be found in the stratosphere and upper troposphere. For about half a century meteorologists have been sending up small balloons carrying recording instruments which measure the temperature and pressure at heights up to 60,000 ft. or more, while recently radio transmitters have been incorporated in the instruments which transmit the temperature and the pressure to the ground station. By following the path of the balloon either by sight or by radio direction-finding, the velocity and direction of the wind at the various heights can also be found. From measurements made in these ways meteorologists have for many years known the general distribution of temperature and winds up to great heights.

Although floatplanes were not popular during the war years, new types have made their appearance since, and presumably, for certain classes of work, more will be seen in the future. With this in mind, this paper is presented in the hope that it may help in assessing the float weights on any new designs that are contemplated. Some suggestions are included concerning geometry and design which, if adopted, may help to show a higher weight efficiency than existing practice.

The paper is based upon an analysis of the weight and geometrical data relating to a large number of floats, although since the number built during recent years is small, a certain amount of data, which might possibly be considered old by some standards, has been incorporated. As will be seen by the curves, recent practice shows no radical departure from earlier years and the inclusion of the early data to establish design trends would appear to be warranted.