An analytical method is presented for the design of two-dimensional contractions. In this method, the complex potential of the flow of an infinite row of equally spaced line sources normal to a uniform stream is obtained. By adjusting the strength of the sources, the streamlines of the main stream are used as boundaries of two-dimensional contractions of various contraction ratios. It is found that, in all cases, there is a region in the main stream between two neighbouring sources in which the speed of flow increases monotonically along streamlines. Contractions formed by any of the streamlines in this region would therefore have favourable pressure distribution along their boundaries except for very small adverse pressure gradient at the inlet and outlet which are due to the introduction of parallel sections.

In the stability analysis of cylinders under external loading, the axial compression and lateral pressure cases are relatively well established: see, for example, ref. 1. However, from a design point of view, a biaxial system of forces due to a combination of axial compression and external pressure is often encountered in launch vehicle structures. While many other combined loading cases have appeared in the literature, the case under present consideration has not; therefore, this note is devoted to a general treatment of this problem. It is to be noted that Radhakrishnan presented some specific results for this loading combination for elastic and plastic buckling.

Using the Donnell equation for small deformations, the present report considers the effect of various compressive loading combinations on the stability problem of an un-stiffened circular cylinder.

Recent studies of the performance of high-speed aircraft have emphasised the importance of engine-airframe integration. For example, Probert and Mallinson, and Bragg have pointed out the advantages of jet deflection in producing extra lift with little penalty in decreased thrust. Townend has drawn attention to producing thrust or lift on high-speed aircraft by external heat addition, and has calculated the effects on the range of the aircraft.

The advent of a new generation of turbojet powered transport aircraft with engines mounted on the rear fuselage has complicated the task of the aerodynamicist, particularly when an attempt is made to determine the individual contributions to the stability and aerodynamic loading of the aircraft. This paper gives some idea of the additional complexity which is directly attributable to the presence of these engine nacelles and their effects on manoeuvring tail loads. Where rational methods are available for determining these effects they are referred to or included.

In the December issue of the Journal some measure of agreement appears to have been reached between Bragg and Smith and the present writer, at least for the second example. The difference of opinion in the first example centres on whether a propelling nozzle with a thrust efficiency exceeding unity necessarily implies perpetual motion. The argument that it does may be put as follows.

Wind tunnel measurements of the auto-rotation characteristics of Lanchester’s “aerial tourbillion” are presented in the form of tip speed plotted against wind speed. Three configurations were tested, a 10.94 inch diameter model with and without a cowling, and a 7.50 inch diameter model without a cowling. All showed a minimum wind speed for auto-rotation, dependent on friction at the shaft. At each wind speed above this value, there were two equilibrium rotational speeds, an unstable one, giving the required initial rpm for auto-rotation, and a higher stable one, the auto-rotation speed, which with increasing wind speed rapidly approached proportionality to the wind speed.

Fairly good agreement with an approximate blade element theory was demonstrated, the best agreement being obtained with the measurements on the model with cowling.

Nadai and Bassali have discussed problems concerning plates supported at several points. Timoshenko and Woinowsky-Krieger have studied circular plates supported at several points along the boundary. In the present note the author has obtained an analytical solution for the problem of circular plates with bending moments applied at several points along the boundary. Some particular cases are also considered.

The solution of some non-self-adjoint eigensystems describing the elastic instability of structural elements requires essentially the determination of the minimum value of a parameter associated with the eigenvalues. Usually, a substantial programme of computation is implicit in this type of system.

During a preliminary consideration of possible methods of practical computation for a certain problem of this kind, which is currently being investigated by the author, the question arose concerning the suitability of a finite-difference approximation for the purpose. The object of such an approximation was to provide a relatively rapid, if crude, means for a first estimate of the solution by desk-calculation methods.

The distribution of stress in a flat plate having a circular cut-out and subjected to known forces at its outer boundary is of considerable practical importance. Assuming that (i) the plate is thin, so that the problem is one of plane stress, and (ii) the material of which it is formed is isotropic and obeys Hooke's law, exact or approximate solutions have been obtained for a limited number of particular cases. Most of these solutions relate to a plate which is infinite in extent in one or more directions. The case of a plate of finite width and infinite length having a circular hole on the axis of symmetry was discussed by Howland, and by Howland and Stevenson. Wang gave an approximate solution for a perforated shear web, and Mindlin investigated the stress distribution around a hole near the edge of a semi-infinite plate under uniform tension.

The drag of an aerofoil is often conveniently measured with reasonable accuracy by traversing pitot and static tubes across the wake of the aerofoil and calculating the drag from either the analysis of Betz or that of Jones.