There have been, in the past, many fatigue tests carried out on a variety of materials and components. These all indicate a wide scattering in the lives (measured by the number of stress cycles to failure) endured by nominally identical components subjected to nominally identical forces before failure occurs. To interpet this scattering several equations have been suggested as representing the statistical distribution functions that fit the lives obtained for individual types of component. Of these functions the log normal distribution function has been perhaps the most widely used. For the central regions of the probability distribution, i.e. about the mean, the log normal distribution and several others represent experimental results very closely indeed, but engineers and designers of all kinds dare not design on the mean fatigue life. They are concerned with specifications that either exclude the possibility of failure or admit only a very small probability of failure. It is thus with the accuracy with which the “lower tail” of the probability distribution curve fits the experimental results that they are concerned.

To assess the fit at this lower end for one type of component, a large number (about 1,000) of aluminium specimens have been tested and the corresponding lives plotted. The results are very interesting. They show clearly that the log normal distribution for this type of component and material is pessimistic for a probability of failure of less than 0·3. This result is felt by the authors to be of very great importance. It has further been shown that the use of the “one-sided censored distribution function”, used previously by one of the authors, gives a curve that will fit the lower results better than the complete log normal distribution would do.

It is with the testing procedure adopted, the specimens used, the distribution functions considered and the conclusions obtained therefrom that this paper is concerned.

The author has previously discussed the flow in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. Yuan has given a solution for high injection in which certain derivatives of the axial velocity become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and that Yuan’s solution is ignoring the shear layer. In this paper the complete solution for large injection is obtained by the method of inner and outer expansions and therefore includes the viscous layer. The resulting series solutions are confirmed by numerical results.

A method of interpolating low aspect ratio lifting surface mode deflections for use in aeroelastic calculations is described. It is based on the spline curve, the numerical analogue of the draughtsman’s spline which is a thin flexible beam used for drawing a smooth curve through a set of given coordinate points. The present problem is one of surface fitting and a matrix scheme using two-way spline curves is adopted. The method of treating the case in which the data points are randomly placed, whilst retaining an exact fit at the points, is discussed, as are the results of a practical example.

Experiments have shown that the drag of a body of revolution with a blunt base can be substantially reduced by mounting behind the body a disc of rather smaller diameter than the body. With a single disc the base drag was reduced by about 35 per cent and with two discs a reduction of 55 per cent was obtained. When the cavity between the body and the best single disc was filled in to form a solid boat-tailed afterbody there was an even greater reduction of drag.

A single disc mounted nearer to the body than the position giving low drag gave a large increase of drag with severely unsteady flow. The nature of the flow in both the low-drag and high-drag régimes is discussed.

A method for the detection of the important modes participating in flutter is presented in this paper. The method is based on energy considerations and is illustrated by numerical examples.

The motion of a solid piston between the driver and test gases in a closed shock tube is studied. In particular, the piston stopping distance, i.e. the total length required to bring the piston to a stop, is calculated for various experimental conditions. Before the stop, the moving piston compresses the test gas, at first with its induced shock and then further with its own kinetic energy through the successive shock reflections. Thus, the moving piston can produce a reservoir of compressed gas with higher enthalpy than a shock of similar strength without the piston. Normal shock-wave theory for an ideal gas is used until the first reflected shock meets the piston. The subsequent shock reflections are approximated by a continuous compression in thermodynamic equilibrium. The calculated values for the piston stopping distance are found to compare favourably with the available experimental data, indicating that the approximations used are reasonable. Peak pressure and temperature of the compressed test gas are computed, and the effect of bleeding the gas reservoir through a nozzle is also included.

An integral part of the study of supersonic combustion is the investigation of supersonic turbulent mixing of dissimilar fluids. Experimental results obtained in the course of investigating the turbulent mixing zone between supersonic streams of CO3 and air are presented. Good correlation between observation and available theories has been obtained in terms of the parameter ξ=σy/x. The correlating parameter σ defines the spreading rate of the mixing zone. The available theories, though not developed for these specific conditions, are shown to be applicable to the turbulent mixing of supersonic streams.

The correlating parameter σ was determined for three different combinations of internal and external flow Mach numbers. The values found for σ were 18, 16·3, 15·3 for constant external Mach number 1·62 and internal Mach number 1·62, 1·53, 1·47 respectively. The magnitudes of σ showed the expected trend, that is the higher value implies the least divergence of the mixing boundaries.

The reasonable agreement with experiment and the simplicity of application of the momentum integral form of solution would appear to favour the use of this approach for the theoretical prediction of the mixing conditions.

A method of deriving the finite-difference equations to be applied at or near flexural discontinuities in plates subjected to bending is suggested. Such equations are presented for the case when a plate consists of two regions of different flexural rigidities, the boundary between the regions being formed by straight lines meeting at right angles.