Thin-walled tubes, in. in diameter, of three hard aluminium alloys and of mild steel have been tested in fatigue under three systems of alternating stresses while subjected to biaxial mean tensions imposed by means of internal pressure. In fatigue under direct or bending stresses the hoop tension in the walls of the aluminium alloy tubes did not seriously reduce the fatigue endurance, but it did markedly affect the mode and rate of crack propagation; cracks initially transverse to the tube axis tended to develop very rapidly in the axial direction. This tendency was present under both fluid and gas pressure, and under gas pressure the cracks propagated so fast that the test piece was often blown to pieces before the gas pressure fell by leakage through the cracks. The gradual taper in wall thickness along the fillets joining the test section to the enlarged ends offered no barrier to propagation of the axial cracks and the whole test piece, including its enlarged ends, was often shattered. Propagation of the axial cracks was preventible by sufficiently reducing the fillet radius, or by a ring glued on. Under alternating torsion, both endurance and mode of failure were affected by internal gas pressure. The initial fatigue crack, either circumferential or axial, often extended over a length comparable with the diameter of the tube, except under low ranges of shear stress when the crack length was sometimes very short. At each end the cracks forked in a characteristic manner and under moderate gas pressure the portions of tHe wall between the prongs of the fork were blown outwards. Under high pressure explosive failure and fragmentation often occurred. Mild steel under alternating torsion with internal gas pressure exhibited the same modes of failure, and two or more fatigue cracks were often formed simultaneously. Under high hoop tension, cracks propagated rapidly and one test piece, after two million cycles endurance, failed by exploding. However, no mild steel test piece was fragmented. A tentative explanation is offered of the reason why, in tubes of small diameter, rather short fatigue cracks may be expected to lead to fast fracture under the static loading. Attention is drawn to the inference that the initial fatigue crack itself must develop very quickly to considerable length.

The effect of a subsonic mean flow on the organ-pipe type of vibration of the air in a duct of uniform area is calculated. The flow at entry to the duct is assumed to be at constant stagnation pressure, and a range of exit conditions is considered. It is found that the effect of the mean flow is to reduce the resonant frequencies by a factor of (1—M2) (where M is the Mach number in the duct) and to introduce damping of the vibration. Except when the duct is terminated by an efficient diffuser, this damping is rather large and it would require a powerful driving mechanism to produce large vibrations in the duct.

Theoretical reaction rate considerations normally require homogeneity of the mixture supply. An attempt—necessarily crude by reason of the analytical difficulties—is made here to cater for the case of non-uniform fuel distribution. Assuming a point-source injector in a parallel pipe, the “loss” in reaction rate is calculated for a limited number of specimen cases.

A theoretical solution is presented for the problem of the clamped circular plate loaded in uniform compression. The solution employs a numerical method programmed for a digital computer. Instead of solving the classical von Kármán large deflection equations, a step-by-step integration of the elastic differential equations of equilibrium is carried out until suitable boundary conditions are attained. The method is an extension of one developed earlier to explain the behaviour of the simply-supported plate.

A method is suggested for designing the shape of the plan form of an unwarped swept-back wing so as to control the magnitude of the singularity that occurs in the chordwise loading distribution at the leading edge. At a Mach number of unity it is possible to do this simply and directly by an approximate application of linearised lifting-surface theory. Details are given of three families of wing plan forms, of varying sweep and aspect ratio, in all of which the strength of the leading-edge singularity is held constant near the wing tips, behind the Mach line from the root trailing edge. The local chordwise load distributions have been calculated in detail for several of these wings and it is found that in all cases the loading curves become effectively independent of spanwise position over that part of the span for which the singularity is constant.