The high speed aircraft whose low speed aerodynamic problems are discussed in this part of the paper belong to the future rather than to the past or present. Küchemann has shown how jet propulsion and the use of a new set of aerodynamics appropriate to supersonic speed lead one from the classical aircraft to new shapes suitable for achieving a required flight range. These shapes include wing-body arrangements with wing sweepback angles of 55° or 60° suitable for a Mach number of about 1·2, and slender, neartriangular wings with sharp leading edges suitable for Mach numbers of around 2 or more, depending on the ratio of span to length.

The possibilities of a vertically-corrugated web as a means of reducing thermal stresses naturally have for some time been generally appreciated by designers. The stress relief to be expected is examined in some detail here. It is shown that quite shallow corrugations can be effective in reducing thermal stress and that a flange-to-web connection at corrugation-pitch intervals can offer substantial advantages over a more continuous type of connection. Arguments are presented to show why straight-sided corrugations are superior to curved ones.

The problem of designing a three-dimensional contraction arose recently in the course of the projected construction of a new low-speed (200 ft. /sec), closed-return wind-tunnel at the Northampton College of Advanced Technology. A three-dimensional contraction was required of contraction ratio 7·4:1 to provide smooth low turbulence conversion to the working section speed within an axial length of 126 inches. The inlet and outlet (working-section) dimensions are shown in Fig. 1 and the sections are similar. It was decided to design the contraction on the basis of an equivalent axi-symmetric contraction whose inlet and outlet circular areas are equal to those of the corresponding irregular octagons and then adapt the derived contraction wall profile to the actual sectional contours. The resulting equivalent inlet and outlet radii are then 55·4 in. and 20·4 in. respectively. The problem was thus reduced to the design of an axi-symmetric contraction of given area ratio within a specified axial length, with favourable velocity characteristics for low turbulence flow in the working section. This latter specification implies the absence of adverse pressure gradients on the walls near the working section and a small percentual difference between axial and wall velocities at the inlet to the working section.

Structural failures have been experienced recently in some panels of relatively thin plating, dished to about twice the plating thickness, and failure has been attributed to snap-through buckling.

Snap-through buckling may be defined as the lateral instability of a dished panel when loaded on the convex side. (Such an effect js frequently observed in the lids of biscuit tins.)

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

There is a considerable body of literature which is concerned with plates having straightforward plan forms, for example circular and rectangular plates have been studied extensively. When the edges are irregular relatively little work seems to have been done, although plates having single notches have been studied and a useful bibliography is found in reference . As far as the present author is aware, the problem of plates built into irregular boundaries has not been tackled.