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 flow near the trailing edge of a circulation-controlled aerofoil is studied. The circulation is controlled by tangential blowing around the bluff trailing edge of the aerofoil.

Velocity profiles in the blowing jet on the trailing edge of a circulation-controlled aerofoil have been measured and a calculation method has been developed for this type of circulation control. The development of the blowing jet is calculated by means of a velocity-profile equation, an angular-momentum integral equation, and an entrainment equation. Improved criteria are suggested for establishing the starting conditions for the development calculation. A realistic method is presented for taking into account the effects of the boundary layer which develops upstream of the blowing slot. A separation criterion for turbulent wall jets and a curvature correction for the entrainment rate are proposed. The calculated blowing-jet developments are found to be in good agreement with experiment. There is fair agreement between the calculated and measured blowing rates required to produce given lift coefficients on the aerofoil.

Recently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Measurements have been made of laminar and transitional heat transfer rate distribution on a 15° semi-vertex angle, spherically blunted, cone at Mach numbers 8·6, 10·6 and 13·0. The laminar results are compared with theoretical predictions and good agreement is obtained with a modified form of the analysis due to Lees. Using a development of the correlation of pressure distributions previously obtained by the author, a new correlation of experimental and theoretical heat transfer results is suggested. The effect of nose bluntness on boundary layer transition has been observed both from flow visualisation and heat transfer results. It is suggested that the main factor causing nose bluntness to influence transition is the adverse pressure gradient which is induced.

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.

A method of analysis is presented for the shear stiffness of a flat-sided corrugated web, attached at a series of discrete points to flanges either on one side or on both sides of the web. Simple expressions are obtained for the shear stiffness of both types of web, and it is shown that there may be a considerable loss of stiffness due to the method of attachment. A comparison is made with experimental results for corrugated webs with both types of attachment.

A theory is presented for the airflow and power requirements of a compressible hovercraft jet operating under equilibrium conditions. It is shown that, even for a partially sonic jet, these requirements may not differ markedly from those of an incompressible peripheral jet.

The buckling behaviour of elastic beams, plates and shallow shells must often be investigated by calculating the slope at the instant of buckling of a curve relating the applied loading and the deformation parallel to the undeformed middle surface. This paper demonstrates the circumstances under which this slope can be calculated exactly without taking into account changes in the mode shape as the buckle amplitude increases.

Recently Messiter has proposed a first-order correction to simple Newtonian theory for the pressure distribution on the lower (compression) surfaces of lifting conical bodies. Although the basic theory holds for bodies with and without attached shock waves, solutions have so far only been obtained for bodies with detached shocks. In the present paper an approximate method of applying the theory to bodies with attached shocks is given. In spite of the approximations involved the calculated shock shapes and pressure distributions are in good agreement with some exact solutions for flat wings, except near the incidence for shock detachment. Like the detached shock case, the present solution can be applied to Nonweiler wings in certain off-design conditions. The combined results for the detached shock and for the attached shock enable the off-design behaviour of Nonweiler wings to be discussed in a systematic manner.

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.

This paper is concerned with the local buckling of long thin flat-walled structures, such as integrally stiffened panels or corrugated core sandwich panels, loaded in such a way that the individual flats are in combined uniform longitudinal compression and shear. When buckling occurs the line junctions between adjoining flats remain straight, and the flats are subjected on their long edges to sinusoidally varying edge moments. These produce sinusoidally varying edge rotations which, when shear is present, are in general out of phase with each other and with the moments. Relations between the edge moments and rotations are obtained in terms of two stability functions, one of which is real and the other complex, to take account of phase differences. Explicit expressions are derived for these stability functions and tables are included, giving their values for the case of pure shear.

Detailed evaluation of the laminar boundary layer parameters and velocity distribution at separation is given. The analysis takes into account the definite variation in separation profiles observed both theoretically and experimentally. The strong dependency of the shape of the separation profile on the previous history of the boundary development is demonstrated.

The well-known Routh-Hurwitz stability criteria apply to polynomial characteristic equations with real coefficients. Lesser known criteria were devised by Hurwitz for the case of polynomials with complex coefficients. However, when polynomials with real coefficients and even powers only are directly subjected to the first-mentioned criteria, all the test determinants obtained vanish identically and thus fail to indicate the state of stability. In the present paper, the stability test functions for such characteristic polynomials are derived.

In this note a relation is established between the correlation parameters obtained by Cohen and Reshotko from similar solutions of the compressible laminar boundary layer, and the Pohlhausen-type pressure gradient parameter used in the approximate methods devised by Luxton and Young. A simple graphical procedure is presented to allow heat transfer coefficients to be obtained from known skin friction coefficients in the presence of a pressure gradient. In view of the restrictions of the similar solutions it cannot be claimed a priori that the method gives accurate results. It does, however, reflect the strong dependence of the heat-transfer skin-friction relation on the pressure gradient and, by reference to calculated results published previously, it is suggested that the method may give adequate accuracy under quite severe conditions.

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.

An experimental study of bow-wave trajectories for a sphere in CO2 has been made in a shock tube, using a drum-camera-schlieren technique, for incident shock Mach numbers of 2·4, 2·8 and 4·0. Results show that vibrational relaxation has only a slight effect on the bow-wave formation time but significantly affects the stand-off distance in steady flow.

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.

The solution has been obtained for the problem of a uniformly compressed and symmetrically loaded circular ring plate of linearly varying thickness. Four particular cases have been discussed and numerical values of the maximum deflection have been obtained for various sizes of the hole of the ring.

The finite element method is extended to the problem of finite plane strain of elastic solids. A highly elastic body subjected to two-dimensional deformations is represented by an assembly of triangular elements of finite dimension. The displacement fields within each element are approximated by linear functions of the local coordinates. Non-linear stiffness relations involving generalised node forces and displacements are derived from energy considerations. For demonstration purposes, the non-linear stiffness equations are applied to the problems of finite simple shear and generalised shear. For finite simple shear, it is shown that these relations are in exact agreement with finite elasticity theory. Convergence rates of finite element representations of these problems are briefly examined.

The Rayleigh-Ritz finite element method is used to obtain an approximate solution of the exact non-linear energy functional describing the large deflection bending behaviour of a simply-supported inextensible uniform beam subjected to point loads. The solution of the non-linear algebraic equations resulting from the use of this method is effected, using three different techniques, and comparisons are made regarding the accuracy and computing effort involved in each. A description is given of an experimental investigation of the problem and comparison of the results with those of the numerical method, and of the available exact continuum analyses, indicates that the numerical method provides satisfactory predictions for the non-linear beam behaviour for deflections up to one quarter of the beam’s length.