An investigation has been made to determine the positions and directions of initiation and the directions of propagation of fatigue cracks and to examine the correlation between these positions and directions and the planes on which maximum tensile and maximum shear stresses are generated.

To afford as wide a range as possible of the ratio of maximum shear stress to maximum tensile stress, tests have been made under combinations of alternating bending and torsion; and in order to separate partially the regions of high shear stress from those of high direct stress, the tests have been made on pieces of square section with the plane of bending parallel to one diagonal of the section. Two series of tests have been made; one a preliminary series on pieces having no parallel portion and the other on pieces having a parallel portion about three times the length of the side of the square section. The positions and directions of initiation and the directions of propagation of fatigue cracks have been observed and compared with the positions and directions of the maximum tensile and shear stresses.

Fatigue cracks may be initiated as a result of either high shear stress or high tensile stress and in the present series of tests on mild steel, cracking in tension has occurred in preference to cracking in shear when the ratio of the tensile stress range to the shear stress range has exceeded about 1.6; for values of this ratio less than 1.6, the cracks started in shear (and vice versa); propagation along the plane of maximum shear appears to be preferred up to a slightly greater value of the tensile/shear ratio (about 1.7 possibly). The general direction of a crack formed as a result of high tension usually follows the plane of maximum tension and that of a crack formed as a result of shear usually follows the plane of maximum shear. In detail both types of crack—in this mild steel—deviate quite widely from their general directions but this deviation bears no obvious relation to the microstructure of the material. Cracks propagating along one plane of maximum shear occasionally show a marked tendency to branch along the associated plane of maximum shear; but this tendency is not always observed and in other cases no tendency to branch has been noted.

A simple theoretical analysis is given of the quantities affecting the sensitivity and range of a schlieren apparatus. In regions of large density gradient the deflections of the light rays may lie outside the normal working range. When this occurs, dark regions may appear in parts of the photograph that would normally be light. Examples of this effect are given, and it is shown that confusion can be avoided by taking photographs in pairs, with the knife edges or slits arranged to give sensitivities of opposite sign.

The deflections of light rays in various typical disturbances in a supersonic air stream are calculated, using geometrical optics. Prandtl-Meyer expansions, boundary layers, and plane and curved shock waves are considered. From these calculated deflections it is shown that some of the anomalous effects commonly observed in schlieren photographs can be explained.

The scheme for taking a pair of photographs of opposite sensitivity for each flow is a useful one in certain problems, but is unsuitable for use in a routine experiment (in which several hundred photographs may be required) because of the additional labour and expense involved. This is particularly so because, apart from resolving any ambiguity which may occur in regions of intense density gradient, the second photograph usually will not give much additional information about the flow. Moreover, the scheme does not overcome the other difficulties associated with the use of an apparatus having inadequate range. The most serious of these is that the apparatus is unable to differentiate between the strengths of density gradients when they exceed the value which deflects the image of the light source completely on to, or away from, the knife edge. Photographs illustrating this effect are reproduced in Ref. 1; the use of inadequate range (i.e. too much sensitivity) is a common fault in wind-tunnel photographs.

A simple system is considered in which a two-dimensional aerofoil in an air stream performs a coupled oscillation in pitching and vertical translation. An expression for the energy transferred from stream to aerofoil is derived as a function of the frequency parameter, amplitude ratio and phase difference, and the conditions under which positive energy can be extracted from the stream are investigated. The connection between the case of zero energy transfer, and the critical flutter state is noted.

Attention is confined to the incompressible case and diagrams show the results obtained when the air loads are obtained from (i) vortex sheet theory and (ii) the classical set of constant derivatives.

Vortex sheet theory leads to the conclusion that, provided that the amplitude ratio and phase difference satisfy certain conditions, energy can be extracted from the stream for all values of the frequency parameter. On the other hand, the use of a set of constant derivatives places an upper limit on the values of the frequency parameter for the extraction of energy.

A method is developed for the calculation of the aerodynamic forces acting on a “swallow tail” wing (Figs. l(a) and l(b)) of small aspect ratio. For a given incidence, lift and induced drag coefficient are, within the limits of the theory, proportional to aspect ratio and independent of Mach number. The exact solution is derived for the limiting case of small sweepback of the trailing edge. A numerical method is indicated for the more general case.

Four buckling problems are considered, namely: —

• (a) A rectangular orthotropic plate, with all edges simply supported, subjected to compression on its ends and a known compression or tension on its sides;

• (b) the same as (a) but with the ends clamped and sides simply supported;

• (c) a rectangular orthotropic plate, with the ends simply supported and sides clamped, subjected to compression on its ends; and

• (d) the same as (c) but with all edges clamped.

In each case it is shown that the variables involved can all be combined into such a non-dimensional form that a single curve serves to give the value of the end compression required to cause buckling. This curve is identical with the curve of buckling stress coefficient against side ratio for a corresponding isotropic plate under uni-axial compression.

Experimental work is described showing that a major cause of changes in the calibrations of hot-wire anemometers consists in the precipitation of dust on the upstream surface of the wire during use. A simple means of cleaning the air in closed-circuit wind tunnels is described. The rate of change of calibration due to dust was reduced in the Manchester University Fluid Motion Laboratory by at least a factor of 15, by adequate cleaning of the air and by minimising the amount of interchange between the tunnel air and the atmosphere. It is concluded that where accurate results are required from hot wires used in a wind tunnel, the tunnel should be designed to be dust-free.