This paper concerns the boundaries between flow regimes for sharp-edged delta wings in supersonic flow and the relation of some predictions of thin-shock-layer theory to these boundaries. In particular, it is shown that the theory predicts that the attachment lines on the lower surface of a thin delta wing at supersonic speeds suddenly jump from just inboard of the leading edges to the centre line in certain flight conditions. In general there is close agreement between the conditions for this jump and the flight conditions corresponding to the change-over from attached flow to the leading-edge separation on the upper surface. Since the movement of the attachment lines on the lower surface must change the position of the sonic line and the nature of the expansion around the edge, it is suggested that the two phenomena are directly related. Thus thin-shock-layer theory can be used to establish the boundaries of the various flow regimes for a wide range of Mach number, incidence and wing sweep. The theory can also be used to predict the effects of wing thickness on leading-edge separation, but here the experimental data is very sparse and somewhat contradictory, so the value of the prediction in the case of thickness requires further investigation.

An experiment was made on a turbulent boundary layer with adverse and favourable pressure gradients alternating twice along the stream. The most important findings of the present study are as follows. In the region of the adverse pressure gradient downstream of the strong acceleration, an internal boundary layer develops within the boundary layer. In this internal layer large advection of turbulent energy occurs and the flow is locally non-equilibrium even near the wall. As a result the usual logarithmic law and turbulence similarity in the viscous sublayer break down.

This study is an investigation of the non-linear behaviour of an elastic spherical cap under the assumption of axisymmetric deformation. The types of axisymmetric loading under consideration are partially loaded uniform pressure, line load, “cosine” load with the maximum intensity at the apex and the combined action of uniform pressure and line load. The edge of the cap is assumed to be rigidly clamped, hinged, and unrestrainedly simply-supported. The method of solution is an extension of the iterative procedure for the integral equations formulated by Budiansky for uniformly loaded, clamped caps. In the cases of hinged and unrestrainedly simply-supported edges, the critical loads for the axisymmetric snap-buckling are presented for different types of loading and various values of the geometrical cap parameter. In the case of a clamped edge the load-deflection curves are established until no solution can be found for further increasing the load. The load corresponding to the limit point on the load-deflection curve is the critical load if the axisymmetric snap-buckling exists. The graphical results are presented for load-deflection curves, deflection profiles, bending moments, transverse shear and interaction of buckling pressures and buckling line loads. The present results are in good agreement with available data for uniform pressure distributed over the entire surface of the cap with three sets of edge conditions and over the central portion of a clamped cap.

Among the many problems which face airframe manufacturers, cooling is certainly one of the most important, particularly as a special watch must be kept on the type of solution to be adopted, since the lowest fuel penalty must be incurred in flight.

A theory is developed for the prediction of the pressure at the reattachment point in subsonic two-dimensional steady base flow. Theoretically estimated values of the reattachment pressure seem to agree well with experimental ones.

Unsteady high Mach number flows past oscillating cones and oscillating wedges are studied according to Newtonian impact theory, with and without centrifugal force corrections. It is found that, contrary to existing theories, the centrifugal force contribution in unsteady flow is significant and not negligible; for example, it contributes one-half to the dynamic stability derivatives of an oscillating wedge and one-third to that of an oscillating cone. It is also shown that in both cases the dynamic stability derivatives calculated by Newtonian impact theory with centrifugal force correction agree exactly with those obtained by gas-dynamic theory in the double limit γ → 1 and M∞ → ∞, independently. These conclusions are expected to hold for more general three-dimensional unsteady Newtonian flow when the Newtonian shock layer is attached.

A numerical method for the solution of three-dimensional supersonic flows and the associated computer programme have been devised. The present algorithm is based on a reference-plane characteristic network. The physical region between the shock wave and the body surface is replaced by a computational mesh facilitating the incorporation of different boundary conditions and arbitrary body shapes. For reasons of stability and computing time a Hartree-type grid was used where the characteristic segments are projected upstream. The base points do not coincide with nodal points and interpolation by means of Tchebycheff polynomials is required to obtain the flow properties. Numerical differentiation is carried out by means of spline functions. The programme has been used and verified under a wide variety of flows past circular and elliptic cones, tangent ogives and a delta wing body. After a series of numerical experiments it was found that accurate solutions could be found using a 7 × 7 grid, and that the essence of the solution is preserved using a very coarse mesh of 4 × 4. Furthermore, the good agreement obtained with experimental results indicates that it could be applied successfully to problems of practical interest.