If it implied anything in the context of high performance turbine engines, the mutilated quotation from “The Hound of Heaven” might conjure up a vision of afterburning turbojets, or turbo-ramjets, propelling second or third generation supersonic transports at very great heights. This would be a misleading picture, and it will probably emerge that the quotation has little to do with what follows, as this is largely concerned with subsonic flight—on which I believe the economic future of aviation will depend for many years.

Published statistics reveal an approximate six-fold increase since 1951 in commercial air transport activity over the North Atlantic. Scheduled passengers increased in number from 341,000 in 1951 to 1,919,000 in 1961; cargo increased from 7,700 tons to 53,000 tons; and mail carriage increased from 3,900 tons to 17,000 tons over the same period. For 1962 a further increase of 12 per cent in passenger traffic and 14 per cent in cargo is forecast. This rapid growth situation has not been accompanied by a corresponding increase in profits, however, as evidenced by a loss estimated in the millions in 1961 on the North Atlantic by the United States international air carriers alone, and an indeterminably greater amount by the foreign air carriers operating in this area. From the limited financial data available, it appears that, among all North Atlantic scheduled international air carriers, only Irish Airlines and Pan American experienced profitable operations for 1961.

When atmospheric testing of nuclear devices was resumed in the latter part of 1961 it was found that certain commercial aircraft were being contaminated by airborne radioactive debris to such a degree that decontamination was required, with associated protection of personnel. Some airlines seemed reluctant to publish detailed information on the position. BOAC, however, recognised the phenomenon as a virtually permanent one and in recent months has been setting a lead in developing the process of measurement and control from a somewhat academic exercise to a properly understood engineering routine. When the nature of the hazard is understood—and particularly the all-important distinction between external radiation and internal radiation—it can be seen that, in fact, passengers and crews are not at risk at all, and that handling and maintenance personnel need not be concerned if the contaminated surfaces are washed by an essentially wet process and personal hygiene rules are observed where necessary.

The main objectives of Missile Evaluation Trials are a complete evaluation of the operational performance of the missile tested, a comprehensive assessment of the practical implications of regular operation of the weapon system from the user's point of view, and the feedback of scientific information to assist in future designs. This means that the trials must be planned to provide data on the following aspects: —

• (a) Scientific evaluation, i.e. determination of performance in the various conditions which will arise in operational use.

• (b) Technical evaluation, i.e. assessment of the detail design, workmanship, engineering and reliability and its influence on operational performance.

• (c) User evaluation, i.e. a practical critical examination of (and evolution of) handling and servicing procedures, personnel training requirements, installation requirements, logistics, and the numerous organisational steps necessary for the introduction of a new weapon into service.

Provided the relationship between the form-parameters H32 and H12is known, the two-dimensional turbulent boundary layer may be calculated by means of the approximate theories of Walz and Truckenbrodt without the necessity for an explicit law for the velocity profile. This relationship H32=f(H12) introduces the influence of the velocity profiles into the calculation. It is the third empirical relationship—beside those for skin friction and dissipation— which is needed to solve the momentum and energy integral equations. The formulae or curves for H32=f(H12) which are given in published papers show considerable deviations from each other so that it was felt necessary to investigate this relationship again. Fig. 1 shows the different curves.

There are many problems in practice, particularly in the fields of buckling and vibration, where the required end result is a curve showing the relation between the eigenvalue and one or more of the basic parameters of the physical system. For example, the curve relating the buckling stress and side ratio of a rectangular plate, with some specified set of edge conditions, under uni-axial compression may be required. Or the problem may be the buckling of a rectangular plate of given proportions, under combined compression and shear, and the determination of the relation between the two types of load at buckling. Alternatively, the effect on the frequency of vibration of varying a concentrated mass, or the stiffness of an elastic constraint at a given point in an elastic system may be required.

The shear stiffness of a beam in bending is commonly determined by measuring the central deflection δ in a three-point loading test for a range of values of the span L under a constant central load. The value of bending stiffness, EI, and shear stiffness, GA, can then be obtained by plotting δ/L against L2 and drawing the best straight line through the points so obtained. The slope of this line for unit central load is then 1/48EI and its intercept on the δ/L axis is 1/4GA on the simple “Engineer's” theory.

The Galerkin method for the approximate solution of elasticity problems (see e.g. Ref. 1) is usually presented as an alternative to the Rayleigh-Ritz method. The main distinction between the two methods is stated to be that the former begins with an equation of equilibrium, whereas the latter begins with a total potential energy expression. The two methods are not always equivalent, and the conditions for equivalence are given in Duncan's lucid presentation of the method (Refs. 2 and 3, which unfortunately have been out of print for some time). These conditions, however, are generally omitted from discussions of the Galerkin method, and it is the purpose of this note to re-emphasise them in a slightly different form.