By considering the equations of motion it has been shown that the flow in the outer part of a two-dimensional, curved, turbulent wall jet is approximately self-preserving if the ratio of jet thickness to wall radius of curvature is constant along the jet. This condition is satisfied for a jet blowing over a surface of logarithmic spiral profile, for which the radius of curvature R increases linearly with distance s along the wall.

Measurements of velocity profiles and rates of growth of wall jets for surfaces with curvature ratios and 1 are presented. These are compared with solutions obtained using an eddy viscosity theory, and with the flow of jets round circular cylinders. The measured jets are found to be approximately self-preserving in form, and to have rates of growth which are much larger than the jets on circular cylinders with corresponding values of s/R.

This paper presents an approach to the determination of structural member sizes to provide minimum weight under a number of load conditions consistent with specified limitations on stress and displacement. The procedure amalgamates the disciplines of matrix displacement analysis and operations research into a scheme suitable for automatic digital computation.

Experiments are described on the interaction of the shock wave generated by a wedge in a supersonic wind tunnel with the turbulent boundary layer on the side wall. It is shown that the onset of separation appears to be largely affected by the action of streamwise vorticity in the interaction region. A simple approximate theory based on this concept shows reasonable agreement with the experimental results. Comparisons have been made with two-dimensional interactions of normal shocks and boundary layers, but they did not produce any conclusive results.

An approximate method is presented for the calculation of heat transfer rates to cooled turbine blades. The method is based on a combination and extension of methods which have been developed in recent years for the calculation of the skin friction and heat transfer coefficients on wings in high speed flight. The use of the method is demonstrated by application to a specific cascade for which an experimental determination of overall heat transfer coefficient is known. Very close agreement with the experimental results is found over the range of Reynolds number tested. The calculated distribution of local heat transfer coefficient indicates that local pressure gradients have a marked effect on the heat transfer. A first-order estimate of the effect of blade cooling on the rate of mass flow through a blade passage shows that an increase of the order of one per cent in the mass flow rate may be obtained by a reasonable degree of blade cooling.

The possible steady rates of roll of an aeroplane are determined in the case when inertia cross-coupling is present. This phenomenon not only changes the simple linear relationship between aileron angle and rate of roll, but may lead to more than one possible rate of roll for a given aileron angle. Simplified equations of motion are given for the cases in which the rolling takes place (a) from level flight, (b) during a pull-out manoeuvre. In both cases, these equations, which are non-linear, are solved numerically for typical examples. The static stability of the possible steady motions is considered in detail, and the dynamic stability is determined in the numerical examples.

A scheme that uses an implicit system of finite-difference equations to obtain solutions of the equations governing the two-dimensional supersonic motion of an inviscid gas is described. The method relies on pseudo-viscosity in order to calculate shock waves. Compared with characteristics methods, pseudo-viscosity methods have certain advantages. For example, shock waves are calculated automatically without special procedures and pseudo-viscosity methods are easily generalised so that problems with three or more independent variables may be considered. Pseudo-viscosity methods have not been used extensively in the field of aerodynamics, partly because of the difficulty in obtaining sufficiently accurate solutions in the neighbourhood of a boundary. The main purpose of this paper is to show how this difficulty can be overcome. The problem of integrating the equations of motion when a boundary condition has to be satisfied on an arbitrary curve is considered. Streamlines are used as one of the independent variables so that the boundary curve is a coordinate curve, and the equations of motion are used in a form which leads to a simple procedure at the wall. For a given system of partial differential equations it is possible to introduce pseudo-viscous terms in many ways, not all of which are satisfactory. The results presented show that the method proposed in this paper is adequate. The calculated results are accurate and vary smoothly in the neighbourhood of the boundary.

A theoretical solution to the initial buckling under shear stress of a long clamped plate with parallel edges reinforced by a stiffener mesh is obtained. The mesh is formed by two families of stiffeners each evenly spaced. One family consists of longitudinal stiffeners parallel to the edges of the plate and the other consists of diagonal stiffeners inclined to the parallel edges. The flexural and torsional rigidity of the stiffeners are included in the analysis. Numerical results are given for the special case in which the longitudinal stiffeners are absent and the diagonal stiffeners have flexural rigidity only.