A number of results derived by the author in earlier reports on the flow of air around blunt bodies moving at high speed are here collected in a unified analysis. The theory predicts in a satisfactory way the shock shape and detachment distance for two blunt bodies, a flat disc and a sphere. It is shown that the density ratio across a normal shock is a useful parameter, combining the effects of both the free stream Mach number and the ratio of specific heats.

The natural transverse vibrations of a long cylindrical box of doubly symmetrical rectangular cross section are considered. Explicit stress-function solutions are obtained for the webs and the top and bottom surfaces so that the effects of shear lag and shear deflection are inherently included. The results are expressed simply in terms of an effective flexural rigidity, which may be determined with the aid of a number of graphs.

A model for the calculation of the “off-design” performance of turbo-machines has been suggested by Mellor, who proposed that the machine be split into an infinite number of stages, each producing a small change in stagnation enthalpy. This note suggests that the overall performance of a machine may be obtained in an integral form which permits a rapid calculation of performance maps for rotational speeds and flow rates not greatly different from design values. The method may be of use in preliminary design studies of multi-stage compressors and turbines.

A simple matrix method is presented for the deflection and stress analysis of cylindrical shell structures of arbitrary cross section stiffened by flexible frames. The method is an extension to fuselage structures of the Matrix Force Method developed by Argyris, in which the internal load system in the structure consists of two parts:—(a) synthetic load distribution, represented by the matrix b0, satisfying the external and internal equations of equilibrium, and (b) self-equilibrating load systems, represented by the matrix b1, which are introduced to satisfy compatibility conditions. The magnitudes of these self-equilibrating load systems are determined from the generalised compatibility equations formulated using the flexibility matrix f for the un-assembled elements of the structure. The self-equilibrating systems are non-orthogonal, but are arranged in such a way that the mixing between one system and another is kept to a minimum and, consequently, the resulting compatibility equations are well-conditioned. The three basic matrices, b0, b1; and f, are compiled using only very simple formulae. The matrices b0 and b1 depend on the geometry of the structure, while the flexibility matrix f is a function of geometry and elastic properties. The present analysis is applied to cut-out problems in fuselage structures. It can also be used for problems involving thermal loading and diffusion of loads in curved panels stiffened by flexible frames.

It is shown from elementary considerations that the lift coefficient of a thin two-dimensional wing at zero incidence, with a narrow high-velocity jet of momentum coefficient Cj issuing from its trailing edge at a (small) downward inclination τ, is given by

and the loading on the chord line (0<x<1) by

(except in a certain neighbourhood of the trailing edge), for small values of Cj. These formulae agree well with known measurements. Interpolation formulae for derivatives of CL at larger values of CJ based on earlier work, are also given: