The 882nd Lecture to be given before the Royal Aeronautical Society was held under the auspices of the Glasgow Branch on 23rd April 1953. Professor W. J. Duncan, F.R.S., F.R.Ae.S., President of the Glasgow Branch, welcomed the visitors. He expressed regret that the President of the Society, Mr. G. H. Dowty, F.R.Ae.S., was unable to be present and welcomed Mr. N. E. Rowe, C.B.E., F.R.Ae.S., Chairman of the Branches Committee, and the Secretary of the Society, Dr. A. M. Ballantyne, T.D., A.F.R.Ae.S.

Mr. Rowe, taking the Chair for the rest of the meeting, said how much the President regretted not being present; as they knew, he had shown the liveliest interest in the Branches and had made many visits to them during his year of office. This was the twelfth Main Society Lecture to be given at a Branch meeting; the holding of Main Lectures at the Branches had proved a great success and he was sure that the present meeting would be a success also, because their lecturer had been doing pioneering work for the past three years on the development of the Comet. After graduating from Cambridge in 1940 Captain Majendie joined the R.A.F. and served as an instructor for several years; he served with Coastal Command in 1943 and was mentioned in despatches, then served on ferry duties, and in 1946 joined British Overseas Airways. He held a Pilot's “B” Licence, a Navigator's Licence and a Wireless Operator's Licence. Before being appointed to work on the Comet he had been engaged in helping Mr. E. S. Calvert at the Royal Aircraft Establishment to develop the high intensity lighting system. Captain Majendie was one of those rare people who combined a scientific and a really practical ability.

In opening this discussion on fatigue it seems that my first duty should be to state what fatigue is – I wish I knew. Just as Alice knew that if you drank much from a bottle marked “Poison” it was pretty sure to disagree with you sooner or later, so do we know that if a component be subjected too often to too high a load it is pretty certain to develop fatigue cracks sooner or later.

It is important to remember that Lewis Carroll was by profession a mathematician, because in a mathematical sense even these heavily conditioned statements should in fact convey a great deal. “Too often to too high a load” infers range of loading, and furthermore it implies a connection between range of load S and cycles N, by which in general N may be expected to increase as S decreases. “Sooner or later” indicates that N is not a unique function of S, and “pretty certain” provides for those pieces which, like certain batteries, obstinately go on long after the others have stopped. Then, lastly “to develop fatigue cracks” is a careful avoidance of a direct reference to failure.

The term “fatigue” is given to the progressive failure of a metal under the repeated application of a cycle of stress. Although investigators have been working for more than a hundred years to determine the mechanism by which fatigue failure occurs, the problem is still not fully understood. The simple slip theories of Ewing and Rosenhain in 1899, Ewing and Humphrey in 1903 and of Gough and his collaborators from 1923 to 1933 appear now to be only partially true, according to some of the modern theories. These suggest that other factors such as polygonisation, deformation bands and crystallite formations, all play an important part.

The difference in outlook between metallurgist, physicist and designer on the problem of fatigue of metals is due not only to the differences in training and method but also in immediate objective, however closely their ultimate objectives may coincide.

Physicists consider fatigue in terms of crystal structure and composition of the constituents of the crystal, noting in passing that certain types of crystal structures are associated with poor fatigue strength. The metallurgist's prime interest lies in the effect of surface finish, heat treatment, the physical condition of the surface, such as degree of cold work, the effect of carburised and nitrided cases having different hardness from the core. Both think in terms of controlled condition tests, with idealised test conditions such as cylindrical test specimens, close control of changes of section, polished surfaces of only a few micro-inches surface roughness, operating in a controlled atmosphere.

The problem of fatigue in aircraft design is a comparatively new one so far as the airframe designer is concerned. There are three main reasons for its prominence. Firstly, the utilisation rate has increased enormously, particularly with transport types; indeed, the hours flown by a civil aeroplane in a single year nowadays far exceed those in the whole life of a bomber up to the period of the 1939-45 War. Secondly, the increased cruising speeds of modern aircraft have aggravated the loading conditions which give rise to fatigue; and thirdly, the development of modern high strength light alloys has enabled higher ultimate stresses to be used, although the fatigue resistance of the material has not kept pace with its ultimate strength.

This paper reviews work on the flexural centre of elastic cantilever beams and contains a number of hitherto unpublished results, including a formula giving the position of the flexural centre in terms of the Prandtl torsional stress function.

The appearance of the note by Jacobs has prompted the preparation of a review of this subject which is all the more desirable as several of the investigations made shortly before the 1939-45 War were never published and others, although published, seem to be in danger of being overlooked. The present paper contains a number of hitherto unpublished results. The question of nomenclature is worthy of mention since general agreement is lacking. Some of the names used are flexural centre, centre of flexure, elastic centrum and centre of shear but a complete search of the literature would probably lead to the discovery of yet other names. The terms “centre of shear” and “elastic centrum” seem vague and fail to indicate that the point referred to has any special relation to flexure. We shall here use the name “flexural centre” exclusively.

Reading the paper by Tye and Cundall in the June issue of the journal, I was started on a train of thought on the same lines.

I agree with the paper but feel that the argument has not been taken far enough. The main conclusion is:–

So long as a random failure is no more expensive and troublesome than a controlled replacement, it is always cheaper to wait until an item fails before replacing it. This is quite independent of the law of failure with time.

The theoretical aerodynamic properties of supersonic aerofoils of polygonal section are well known. This note describes the results obtained by applying supersonic aerofoil theory to a simple curved aerofoil of arbitrary maximum thickness position, the leading and trailing edges of which are pointed.

The results for a symmetrical curved section are compared with the theoretical properties of a symmetrical double-wedge section.