In this paper the shock waves of a slender aircraft are considered at a great distance from the aircraft so that all the shocks have coalesced into either the bow or rear shocks, but not at such a great distance (asymptotic) that the two shocks are of equal strength. Lower bounds are determined for the pressure jump across the bow shock subject to various aircraft constraints, and the pressure jumps across both the bow and rear shocks are determined at off-design conditions. The work described is considered to be a preliminary investigation and the results are such that further work seems to be warranted.

The nature of flapping torsion flutter of a helicopter blade in forward flight is discussed. The essential complication in the analysis is the presence of periodic coefficients in the equations of motion; approximate solutions are obtained by use of a perturbation procedure. An unusual behaviour of the flutter equations which occurs when the fundamental frequency of flutter is a half-integer multiple of rotational speed is studied. Two different instability mechanisms can be distinguished and are related to the two energy sources in the system, namely the rotation of the rotor and the forward speed of the helicopter. It is found that forward flight can have a significant stabilising influence on flutter and that, as the tip speed ratio increases, flutter occurs predominantly at half-integer frequencies. The results are confirmed by the use of a numerical method.

In this paper a generalised presentation for symmetrically stiffened orthotropic cylinders under compression is developed, based on a linear orthotropic stability theory of cylinders. Similarities and differences in the minimum weight behaviour of stiffened cylindrical shells and flat transversely-stiffened wide columns are investigated in some detail to provide a satisfactory physical picture. The concluding results provide a comparative evaluation of various forms of stiffening systems for cylindrical shells under compression.

The decay of a trailing vortex containing a turbulent core is examined according to the argument that the turbulence is partly sustained by, and interacts with, the irrotational flow through viscous diffusion of eddies across the core boundary. The region separating the core from the outer irrotational flow, in which the interaction between the turbulence and the mean flow occurs, expands with time like (time)1/2, characteristic of viscous diffusion.

On the basis of a simple representation of the radial distribution of mean circumferential velocity, the decay of the vortex is calculated and is found to behave in a way similar to what Squire predicted, on the assumption of a constant eddy viscosity, in 1954. The essential difference from Squire’s solution found here is that the apparent viscosity is not simply proportional to the initial circulation about the vortex as he proposed, but depends on the Reynolds number defined with respect to the circulation.

Wind tunnel and flight observations of vortex decay can be more closely reconciled than Squire’s theory allowed; those differences that exist are attributed to the vastly different ages of the vortices in the laboratory and flight experiments. The principal conclusion of practical interest is that the maximum circumferential velocity in a trailing vortex generated by an aeroplane in flight is

where Γ is the circulation about large circuits enclosing the vortex, v the kinematic viscosity of the air and t the (sufficiently great) age of the vortex.

An energy approach has been used to obtain approximations to the natural frequencies of uniform beams when the effects of shear flexibility and rotatory inertia are included. The characteristic functions of simple beams are used to describe the bending deflection and the necessity for an assumed shear deflection shape has been eliminated by the use of simple relationships which exist between the effects of shear flexibility and rotatory inertia. A comparison of the approximate frequencies with the exact frequencies shows good agreement even at the higher frequencies. The method has been applied to hinged-hinged, fixed-free, free-free, fixed-fixed, fixed-hinged and free-hinged beams.

An initial value method is introduced in this paper for the solution of the two-point non-linear ordinary differential equations resulting from an analysis of the MHD boundary-layer flow originally treated by Greenspan and Carrier. By using this method, the iteration process is eliminated. The method is seen to be applicable to the solution of similar two-point boundary value problems where certain physical parameters appear either in the differential equation or in the boundary conditions and solutions for a range of the parameter are sought.