The paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.

When correcting the measured unsteady aerodynamic forces experienced by an oscillating body for wind-tunnel interference, it is customary to assume that the free-stream conditions ahead of the model are invariant with time. For small, streamlined models oscillating with small amplitudes this assumption is substantially correct. However, for large variations in the drag force on the oscillating body this assumption is imprecise, particularly at low frequency parameters. In the present paper the flow at stations a long way removed from the body section is examined on the basis of the unsteady form of the Bernoulli equation. The predicted free-stream fluctuations are found to be in agreement with experiment.

A theoretical study is made of the aerodynamics of wings executing simple harmonic oscillations. The wings considered are slender and infinite-simally thin; they may have curved leading edges and be cambered, but their cross sections must be straight lines. The value of the reduced frequency is assumed to be such that the flow is governed by the two-dimensional Laplace equation.

Leading-edge separation is simulated by a line vortex joined to the leading edge by a cut. The strength and position of the vortex and the values of the generalised forces can be determined by the theory. Results have been calculated for flat delta wings and a flat gothic wing; they are in reasonable agreement with experiment.

A simple general expression is obtained for the rate of change of generalised aerodynamic damping coefficients with respect to frequency parameter in the limit as frequency tends to zero. The expression is directly proportional to aspect ratio and does not depend explicitly on Mach number. The result is consistent with calculated pitching derivatives from finite-frequency theory.

This extension of quasi-steady theory is applied to determine the leading transient term of the asymptotic expansion for large time of generalised forces due to an indicial upwash field. The expansion has direct relevance to the use of quasi-steady aerodynamic derivatives in the field of stability and control.

This paper presents the application to a number of structural design problems of a procedure for determining minimum weight member sizes. Included are examples of trussed and stiffened plate structures and experience with computational times for a wide range of problem sizes.

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.

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.

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.

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.

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.

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.

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.

A theoretical treatment is considered for the flow past slender wings in sudden plunging motion when leading-edge vortices are present. A form of slender-wing theory is used and, although the basis of the theory involves no restriction on compressibility, it has proved possible to make calculations only for an incompressible fluid.

Use is made of an analogy between the unsteady flow and related steady flows. In the incompressible case, an extension of the theory of Brown and Michael is given to determine the strength of the vortex and its path from the leading edge to the final steady-state position. A qualitative comparison with experiment is made of the instantaneous position of the vortex. In a typical case the lift is calculated to remain within one per cent of its final value after the vortex strength has reached 55 per cent of its final value.

The stress-concentration factor is calculated for an infinite plate in tension containing a doubly-symmetrical hole whose boundary consists of parts of three intersecting circles. A suggestion is made for modifying the results to apply to a strip.