Hypersonic conical flows over delta wings are treated in the thin-shock-layer approximation due to Messiter. The equations are hyperbolic throughout, even in regions where the full equations are elliptic, and have not hitherto been solved for flows with attached shock waves. The concept of the simple wave has been used to construct a class of solutions for such flows; they contain discontinuities in flow variables and shock slope but, for the case of flow over a delta wing with lateral symmetry, agreement with results of numerical solutions of the full equations is good. The method is applied to plane delta wings at yaw, and to wings with anhedral and dihedral. For the flow at the tip of a rectangular wing, it is shown that two distinct solutions may be constructed.

The solution to the problem of the loading generated on a two-dimensional thin aerofoil by an incompressible flow whose normal velocity component is of the general form exp [i(λx+/μy — ωt)] is calculated. The method used extends the two-dimensional integral equation solution for the induced vorticity by means of a Chebyshev expansion of part of the kernel function. Thin aerofoil approximations are made throughout, but no collocation procedure, as such, is required.

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.

A method for the generation of assumed modes in beams with arbitrary boundary conditions is described. The method is applied to two cantilevered beams using a modified Rayleigh-Ritz vibration analysis. The results obtained show excellent agreement with those obtained by exact methods of analysis.

The paper first describes an approximate method for calculating inviscid flows round arbitrary aerofoils at sub-critical Mach numbers, based on second-order theory with empirical improvements to give better agreement with exact theory; several comparisons are shown. This method is then used as the basis of an iterative procedure for calculating the effect of the boundary layer on the surface pressures and overall forces; several comparisons are given with recent experimental results.

Fatigue tests have been made in constant amplitude loading and in narrow band random loading on FV520B steel lugs of width 27 mm loaded by means of a pin 12·7 mm in diameter. The test frequency was 220 Hz, a mean tensile stress of 309 N/mm2 was used and tests extended for endurances of up to 109 cycles.

For endurances up to 106 cycles there was good agreement between constant amplitude and random loading results with both stresses expressed in root mean square values. Beyond this endurance, the random loading results lay below those obtained in constant amplitude loading. Predictions made using the Palmgren-Miner cumulative damage hypothesis in conjunction with the endurance curve in constant amplitude loading gave good agreement with the results in random loading over the whole range of endurances tested.