Before making an appreciation of present knowledge about a single metal, it is not inappropriate to say something of all metals, for the ever-increasing tempo of material civilisation has largely depended on man's increasing knowledge of these constituents of his World. His first discovery in this field was copper. To it and to its alloys he gave an exclusive allegiance for some 100 generations, then about 3,000 years ago iron became, and still continues to be, the predominant metal of his needs.

In the eighteenth century, when alchemy finally gave way to the logic of scientific thought, the metals employed by man for purposes other than currency and decoration were practically confined to iron, copper, tin, zinc, mercury and lead. Today, when over seventy metallic elements are known, only a small number of these are used by the engineer.

There has been considerable activity of recent years, particularly in America, in the field of integral structures for aircraft.

The fundamental problem in aircraft structures is to make a relatively thin skin covering take applied compression, shear and bending loads. This has been achieved so far by the attachment of stiffeners, but this requires a large amount of riveting which in itself causes structural inefficiency and also spoils the smoothness of the skin, particularly when laminar flow is desired. Metal gluing shows great advantages over riveting in this respect but it is doubtful whether the bond strength will be great enough to attach very heavy stringers to very thick sheet. Where structural loadings become higher the required thickness of sheet and stringers may make the continued use of riveting difficult, if not impossible.

The helicopter, because of its complicated nature, provides the mathematician with a delightful set of problems on which to exercise his ingenuity, but the purpose of this paper is to interpret the functioning of the helicopter in terms of its physical aspects.

The paper is divided into three main parts: —

1. 1. General Performance

2. 2. Control and Stability

3. 3. Rotor Vibration Problems.

Consider a cantilever beam of uniform cross section whose generators are parallel to the z-axis and whose lateral surface is free from surface tractions. The line of centroids of the cross sections in the unstrained state is taken as the z-axis, and the x- and y-axes are the principal axes of the cross section at the centroid of the fixed end z = 0.

The other end of the beam (z = l) is subject to forces which reduce to a single force with components (Wx, Wv, 0), transverse to the z-axis, acting through the load point L of this end section (see Fig. 1). The co-ordinates of L are taken as (p, q, l).

The problem of aileron effectiveness when the elastic properties of the wing structure are taken into account has already been adequately covered in the subsonic regime by A. R. Collar and E. G. Broadbent. The method used depends upon strip theory which pre-supposes a knowledge of the relevant aerodynamic derivatives. A unified method has been considered by the present author which employs either the semi-empirical theory of D. Küchemann or the lifting surface theory of H. Multhopp in such a manner that the effective values of the relevant derivatives are found, together with the rolling efficiency.

Compressor stages are usually designed on the assumption that the gas velocity is nowhere affected by the friction at the walls. The only way in which viscosity is taken into account is in the assumed efficiency, and in a guessed “work-done factor,” which ensures that by aiming high the required work is actually attained.

It is known that the radial profile of the axial velocity component becomes more and more peaked through successive stages of a compressor, so that the assumptions just quoted become very inaccurate. It is possible that the efficiency of a stage could be raised considerably if the axial velocity profile were controlled; moreover up to 20 per cent. more work could be done if a “ work-done factor ” did not have to be applied.

Tests were made at the request of the Royal Aeronautical Society Structures Committee to extend the information on Data Sheet 02.09.02 from a value of the parameter.