For boundary layer flows over curved surfaces at moderately high supersonic speeds the existence of normal pressure gradients within the boundary layer becomes important even for small curvatures and they cannot be ignored. The describing equations are basically parabolic in form so that the simplifications inherent in hyperbolic flows would not at first sight seem to be relevant. However, the equations of motion for a two-dimensional, supersonic, rotational, viscous flow are analysed along the lines of a hyperbolic flow and the individual effects of viscosity and vorticity are examined with regard to the isobar distributions. It is found that these two properties have compensating effects and the experimental evidence presented confirms the conclusion that inside the boundary layer the isobars follow much the same rules as those which determine the isobars in the external hyperbolic flow. Since for turbulent boundary layers the fullness of the Mach number profile produces almost linear Mach lines in the boundary layer, this provides a simple extension to the methods of analysis, and the momentum integral equation is reformulated using a swept element bounded by linear isobars. The final equation is similar in form to the conventional one except that the momentum and displacement thicknesses are now defined by integrals along the swept isobars, and all normal pressure gradients due to centrifugal effects are accounted for.

The derivation of a non-linear theory on bending of orthotropic sandwich plates is carried out by the principle of complementary energy from elasticity. The governing differential equations and natural boundary conditions are obtained. The assumptions used are, namely, the facings are orthotropic thin elastic plates with negligible bending rigidities and are made of the same material; the orthotropic core can take the transverse shear only; and the transverse shortening of the core may be ignored. The geometrical non-linearities are equivalent to von Kármán’s theory for single-layered plates. Through the introduction of a “shear function”, the number of differential equations is reduced to three and the equations are in rather simple form. It appears that the equations obtained here would require, comparatively, the least amount of work for analysing the finite deflection sandwich plate problems having a wide range of properties of practical interest.

Using the methods of the linearised theory of supersonic flow, the shape of the pressure curve (or the potential curve) on the root chord of a wing, extending symmetrically from a fuselage of circular cylindrical cross-section, and near its leading edge is calculated in the following three cases: (a) the wing has a rounded leading edge and is non-lifting, (b) the wing is a flat plate at incidence with a supersonic leading edge, (c) the same as (b) except that the leading edge is subsonic. In all cases the fuselage is non-lifting and the plan form of the wing is a half delta. The results in (a) and (b) can be expressed in terms of elementary functions; the results in (b) and (c) are tabulated.

Further details are given of a recently developed triangular equilibrium element which is then applied, in conjunction with the complementary energy principle, to the finite element analysis of some plate bending problems. The element is demonstrated to have a straightforward and satisfactory application and to possess advantages over the conventional triangular displacement element.

Experiments performed on a low-speed circulation-controlled aerofoil are described. The aerofoil was of elliptic section with the circulation controlled by means of a jet blowing around the blunt trailing edge. Results for the lift, drag and pitching moment on the aerofoil are presented as functions of the blowing momentum coefficient and the angle of incidence. The results are for a two-dimensional aerofoil. Possible applications of this type of aerofoil are briefly discussed.

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.

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.