The effects of sting diameter and cylindrical protuberance length on the base pressure of an axisymmetric body in a turbulent supersonic flow are experimentally determined. It is found that the change in base pressure due to the presence of the sting is greater than 4 per cent when the ratio of sting diameter to base diameter is 0·150 or greater. When the ratio of cylindrical protuberance length to base diameter is greater than 1·3 there is no apparent change in base pressure with a change in length. However, when this ratio is less than 1·3, the base pressure varies greatly with length.

This paper provides the basis for a very general approach to the determination of initial buckling stresses of long stiffened panels in uniform longitudinal compression. The panels are assumed to consist of a series of long flat strips, rigidly connected together at their edges, as in panels with top-hat or Z-section stringers, or in sandwich panels with corrugated cores. Whatever the buckling mode, the individual flats are subjected, just after buckling, to sinusoidally varying systems of both out-of-plane and in-plane edge forces and moments, superimposed on the basic state of uniform compression. The stiffness matrices corresponding to these sinusoidal edge loads are derived, taking account of the destabilising effect of the basic longitudinal compressive stress, not only in the out-of-plane but also in the in-plane deformations. For the latter purpose a non-linear theory of elasticity is used. The application of these stiffness matrices to specific panels is briefly described. All possible modes are incorporated within one determinantal equation. For panels with identical stiffeners spaced at equal intervals, the order of the determinant is independent of the number of stiffeners.

A theoretical analysis is presented for a two-dimensional air strut with walls consisting of thin membranes which are joined by many inextensible strings. The strut is deflected through large angles so than an appreciable portion of each membrane is buckled and lies along the solid plates which form the ends of the strut. Numerical solutions are obtained for two cases and, in particular, the resultant force on each end plate is determined.

A probe is described which will detect contamination, by driver gas, of the test section flow in a shock tunnel. It is a continuously sampling device, which responds to the difference between the ambient speed of sound in the driver gas and the test gas. The probe is compact, easy to construct, and can be used for detection of driver gas in routine testing. The theory of the probe is explained, and experiments are reported which confirm its effectiveness.

The wholly supersonic flow past a two-dimensional wedge is analysed on the assumption that release of chemical energy into the stream can be accomplished across a thin discontinuous plane flame front attached to the apex. Forces experienced by the wedge are calculated and representative flow patterns exhibited. Some typical interactions between the flame and shocks or centred simple waves are discussed, with emphasis on the use of pressure-flow-deflection diagrams to obtain results.

This paper presents a method for evaluating the effects of shear flow on the performance of a two-dimensional cascade in an incompressible fluid. The method of distributing the singularities along the chord is modified to meet the requirement that the sum of the distorted and perturbed velocities should produce a flow around the aerofoil; therefore an actuator-disc or flat-plate type approximation is not used. Attention is confined to a single row of arbitrary aerofoils subjected to pure harmonic distortions, no attempt being made to include time-dependent terms. Hence it is probable that this paper offers the first stage of a time-independent solution for assessing the effects of upstream struts or blade rows. The agreement between this method and the exact solution for an isolated flat-plate aerofoil is fairly good.

Numerical examples are presented and discussed with reference to the changes of lift, deviation angle and surface velocity which distortion over the cascade would produce. It is found, for the limited number of examples calculated, that a positively-staggered cascade readily responds to the variation of geometrical parameters chosen.

A differential equation which contains an eigenvalue is considered as a pair of simultaneous differential equations by augmenting the main equation with the equation λ′=0. This ensures the constancy of the eigenvalue λ. The differential eigenvalue problem is thus reduced to a pair of simultaneous non-linear differential equations with two-point boundary conditions. An iterative method for the solution of the two-point boundary value problem is described.

To demonstrate the method, the normal modes and frequencies in flapping of a helicopter rotor blade are calculated. In the case considered the stiffness and mass/(unit length) of the blade have points of discontinuity. The method may also be applied when the blade parameters are given in the form of experimental data.

The Dynamic Relaxation solution of the Laplace equation introduces dynamic terms into the basic equation. When this is written as an explicit finite difference formulation it can be solved by an iterative process which only requires a simple substitution routine. The method is easy to programme and requires small storage in the computer. By studying problems involving wind tunnel interference in steady flow, the potentialities of the method are demonstrated.

General solutions for two-dimensional incompressible potential flow occurring between two equipotential planes perpendicular to the x-axis are given. The first form is the two-dimensional analogue of Thwaites’s solution for axisymmetric flow and allows the calculation of the flow when the axial velocity distribution is specified as a Fourier cosine series in x. The second form of solution, obtained by “inverting” the first form, allows the calculation of the flow when the shape of the “boundary streamline” is specified by a similar series in the velocity potential ϕ.

It is shown how the second form of solution may be utilised to design contracting channels between equipotential planes. The computation of the contraction shapes and velocities is straightforward. In particular, contractions are derived from smoothing conditions similar to those used by Thwaites, and from a flow having a single (ϕ, y) step-discontinuity. It is shown in the Appendix that the latter flow possesses a closed form representation in terms of elliptic functions.

An analytical study is made of the laminar mixing of two semi-infinite streams that are initially parallel. The equations governing the mixing process and the boundary conditions are derived by application of the perturbation technique. The “missing” correct third boundary condition is shown to be the condition that the pressures of the inviscid upper and lower streams due to the displacement thicknesses be balanced across the mixing layer. A general procedure for solution of the mixing problems is established by means of a transformation of the mixing-layer equations and two boundary conditions.

As an example, the laminar mixing of two parallel uniform streams of both incompressible and compressible fluids is solved. It is shown that the profiles of v are entirely different from those based on the approximate third boundary condition. The improved profiles are in excellent agreement with the experimental data.