The paper first discusses the analysis of a general vector field with the aid of the concept of the field line with its tangent, principal normal and binormal. Detailed applications are made to the motion of inviscid and of viscous fluids.

Reversed direct stress and rotating bending fatigue tests have been carried out on Vee-notched specimens of aluminium alloy, nickel chromium steel and mild steel.

Diagrams are presented showing the relationship between the geometric stress concentration factor Kt and the strength reduction factor Kt. It was found that non-propagating cracks formed in the roots of the sharper notches. These cracks formed at or above some critical value of Kt, the value depending on the specimen material. Below the critical value of Kt, cracks did not form unless the applied nominal stress exceeded that at the fatigue limit, and a crack, once formed, continued to propagate until the specimen failed. Above the critical value of Kt, non-propagating cracks formed at nominal stresses less than the fatigue limit, the stress having to be increased to the latter value in order to propagate the crack. This critical value of Kt coincided with the maximum Kf value realised. It would appear that Kf equals Kt up to a certain value of Kt; there is then a transition where Kt reaches a maximum at the critical value of Kt. Increasing the value of Kt above the critical value causes no further increase and may tend to decrease the value of Kt.

The conclusions drawn apply only when the fatigue stresses are completely reversed, i.e. the mean load is zero.

Tests have been carried out on round bar specimens of various strong aluminium alloys (unclad) in the fully heat-treated condition in both tensile and compressive loading. A careful study of the results establishes beyond reasonable doubt that there is a progressive change in the tangent elastic modulus with stress. The variation is appreciably greater than that predicted by the consideration of second-order effects in the conventional stress and strain representation. It is found that the modulus decreases with tension and increases with compression by about 5 per cent at 30 tons/in.2, the form of the variation being a continuous function. Tests on two alloys of aluminium other than those of the normal zinc-bearing and the copper-bearing types were also carried out. The first of these was a simple fully heat-treated binary alloy of 4 per cent copper which was very similar in behaviour to D.T.D.364; the second was a 5 per cent alloy (N.S.6-½H) which, after its initial loading, showed only very slight elastic modulus variation in the subsequent loading and unloading lines. An additional test to compare naturally and artificially aged D.T.D.364 did not reveal any difference in the degree of modulus variation.

In view of the present experimental findings, the use of the “second” modulus line in the proof stress determination of unclad strong alloys should be adopted generally, if practicable. A high level of internal stress can cause slight errors in this method because the elastic limit is then prematurely reached. As an occasional check on the method when applied to routine mechanical testing, the elastic component of strain can be found for the last point on the loading line by returning to the zeroing load.

In the Appendix the difference between true and nominal stress-strain relationships is calculated. The meaning and theory of modulus variation is also discussed and aluminium alloys are compared with a high-tensile steel.

A simple expression for the form of the variation is proposed.

In studies of the stability of aeronautical systems, equations of motion are derived which have coefficients dependent on flight speed. Conventional practice treats the speed as constant, when a set of linear differential equations with constant coefficients results. Actually, since the speed varies during flight, it may be regarded as a prescribed function of time; the set of linear differential equations then has variable coefficients.

The treatment of the problem of stability then becomes much more complex in this case. A simple example is given to show that a system which is stable at any constant speed can become unstable during deceleration; the ordinary constant-speed criteria are, strictly, therefore inadequate. Some approaches to the discussion of stability during acceleration are suggested; a solution is given of the single second-order equation which enables the amplitude of oscillation of the solution to be studied. Inverse methods of approach are suggested, both for single and sets of equations, in which particular forms of acceleration corresponding to prescribed solutions are derived; and some tentative conclusions are drawn. As would be expected, the effects of acceleration depend on a dimensionless “acceleration number.”

The “second stage” two-dimensional jet flap experiments are briefly described and some of the results presented with comments. The relative simplicity of these experiments and the measure of their agreement with the theory provides, it is hoped, yet another illustration of the value of comparatively simple experiments in the early stages of work on a novel idea.

This paper describes a first attempt to establish the order of magnitude of finite aspect ratio effects for jet-flap wings. Lift, pitching moment, and drag results are presented from pressure-plotting measurements on a jet-flap model of aspect ratio slightly less than three. These experiments were complementary to two-dimensional tests carried out at the National Gas Turbine Establishment.

The influence of higher-harmonic deflection components on the creep-buckling characteristics of an idealised H-section column is investigated. The creep properties of the material of the column are defined by a simple power-function creep law. The results show that higher-harmonic deflection components reduce the column lifetime significantly only when their initial amplitudes, as well as the initial amplitude of the first harmonic component, are very large. Furthermore, it is shown that second-harmonic components have a much smaller effect on the column behaviour than do third-harmonic components.

The drag in two-dimensional flow is expressed in terms of the distributions of static and stagnation pressures along a traverse line downstream of the aerofoil. Sources of error are discussed with regard to their effect on the accuracy of drag measurement in small tunnels at medium Mach numbers.

Tests have been carried out on a series of convergent-divergent nozzles and the results compared with those from a test on a convergent nozzle. At the design pressure ratio, reductions in the noise were found, particularly at 90° to the jet direction. For lower forward pressures the noise is also less, but above the design pressure the noise rises rapidly to the same level as that with a convergent nozzle. In the experiments cold jets were used, but the results are probably applicable in certain respects to hot jets.

The aiming problem in aerial gunnery has formerly been analysed by approximate methods which allow results of sufficient accuracy for practical requirements to be obtained from a very simple mathematical treatment. There has therefore been no practical demand for any more elaborate analysis, although the development of a more exact treatment of the problem is not without interest from the academic point of view. In this paper a more complete analysis is developed in a form which is generally applicable to a broader class of aiming problems. The relevant parts of the standard external ballistic analysis for projectiles fired from guns are also included for the sake of completeness, and the earlier simplified analysis of the aiming problem is also presented to allow comparison of the results with those of the more complete analysis. Finally, a section on the gunner's view of the aiming problem is included, to provide an explanation of certain difficulties which frequently arise through neglect of the important differences between the points of view of an observer moving with the gun and an observer at rest in the air.

The compressible flow past an oscillating two-dimensional aerofoil in a wind tunnel with porous walls is considered, using linearised theory. The porous wall is assumed to have the property that the ratio of the normal velocity at the wall to the pressure drop across the wall is constant. Transform theory is used to find the supersonic longitudinal stability derivatives, and an extension of Possio's integral equation for the quasi-stationary case in subsonic flow.

Several plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.

When a non-uniform stream flows through a cascade of compressor blades a three-dimensional secondary motion is generated in the outlet stream. This motion, which consists of a spanwise re-orientation of the Bernoulli planes, together with the effects of vorticity components in the stream direction, may be predicted theoretically. In this paper experimental results obtained on a 6 in. chord cascade are reported. The experimental and computed outlet angles are compared and the discrepancies are explained qualitatively. Additional particle track and visualisation experiments were designed to investigate the local blade flows and the effects of the nose vortices.

By using the methods of the Calculus of Finite Differences, expressions are obtained for the nodal moments and deflections of a simply-supported grillage, subjected to a loading constant along one set of beams and having a sinusoidal variation along the other set of beams. A simple example verifies the expressions and illustrates their use.

A method has been given by Klitchieff for analysis of grillages of intersecting beams under lateral loading. Klitchieff's solution was in the form of infinite Fourier series and the expressions for bending moments converged approximately as Σ n–2, making numerical computation difficult. This paper shows that, for grillages in which one set of beams are evenly spaced, Klitchieff’s solution can be adapted to give finite series for deflections arid bending moments at the intersections of the beams. The number of terms in the series is not greater than the number of beams in the equally spaced set (referred to in this paper as set “ A ”). A numerical example is given and an accurate solution is obtained with appreciably less computation than other known methods would entail.

A systematic discussion of partitioning as a tool for matrix inversion is presented, together with various methods and applications which have been of help in actual computations. New concepts are introduced, among them those of super-matrix and of square partitioning. The most usual type of partitioning, that into 2x2 sub-matrices, is discussed in detail, showing the orderly arrangement of the calculations in an auxiliary matrix. Further sections deal with matrices of the continuant type, and with special types of symmetry in the arrangement of the sub-matrices. The greatest advantage of the method of partitioning for the inversion of these types (as compared with the elimination method) lies in a considerable reduction in the number of arithmetical operations.

A method is presented for the calculation of the streamwise component of vorticity, for flows in rotating passages. The method may be regarded as an extension of the methods applied in recent years to the calculation of secondary flows in stationary passages.

Attention is concentrated on the quantity I=p+½ρV2−½ρU2, where V is the fluid velocity relative to the rotor and U is the rotor tangential velocity. I remains constant along a streamline in the rotor, and is found to enter into the equation for the generation of vorticity in much the same way as the total head enters for flow in stationary passages.

An approximate calculation of the streamwise vorticity generated in a simple axial-flow rotor is made, and qualitative consideration is given to the flow in a centrifugal impeller. Just as for the calculation of secondary flows in stationary passages, an approximate shape of the streamline must be assumed before the secondary flows can be calculated.

An approximate method is described for the calculation of turbulent boundary layers in which the turbulence is developed before the commencement of the adverse pressure gradient, as in most diffuser layers. It is based on a method due to Spence which has been modified and also extended to the calculation of three-dimensional diverging layers such as occur in ducts whose breadth is increasing. The velocity profiles occurring in a diverging layer are examined and it is shown that the inner part obeys the universal logarithmic law, as in two-dimensional layers. This result is used to obtain an equation for the form parameter in diverging layers, by substitution in the equation of motion and incorporation of the equations of momentum and continuity for diverging flow. The form parameter equation contains a term involving the gradient of shear stress at y = θ and values of this term are obtained by the analysis of experimental data and the substitution of known values for all the other terms in the form parameter equation. Values of the term involving shear stress gradient are then correlated in terms of known boundary layer quantities, and the resulting correlation allows the formulation of a step-by-step method for the solution of the form parameter equation. This may be used in conjunction with the momentum equation to predict the boundary layer growth. It was not found possible to effect a satisfactory correlation for boundary layers on lifting aerofoils, in which the turbulence develops within the adverse pressure gradient, and the method cannot be used for the prediction of such layers. The results of a number of calculations are given.

Some new solutions for steady incompressible laminar boundary layer flow, obtained by Gortler, have been used to test the accuracy of two methods which are commonly used to predict separation. A modification of Stratford's criterion for separation is given in this paper and is probably the most accurate and the simplest of all methods at present in use. Modified numerical functions are also given for Thwaites's method of predicting the main characteristics of the boundary layer over the whole surface, which improve the accuracy of the method.