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 K t and the strength reduction factor K t. 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 K t, the value depending on the specimen material. Below the critical value of K t, 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 K t, 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 K t coincided with the maximum Kf value realised. It would appear that K f equals K t up to a certain value of K t; there is then a transition where K t reaches a maximum at the critical value of K t. Increasing the value of K t above the critical value causes no further increase and may tend to decrease the value of K t.

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

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 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.

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.

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.

The differential equation considered is

where all the a’s and b’s are real constants.

The nature of the solution is investigated in the neighbourhood of the singular point and the conditions are found for logarithmic terms to be absent.

The conditions for stability for large values of τ are determined; the system is stable if

are all positive for large values of τ.

The form of the response is considered and its oscillatory (or non-oscillatory) nature investigated. The Sonin-Polya theorem is used to determine simple inequalities which must hold between the coefficients of the differential equation in any interval for the relative maxima of | x | to form an increasing or decreasing sequence in that interval.

Evvard’s technique is applied to the problem of a thin finite wing moving at a supersonic speed when the leading edge is subsonic. It is developed in two methods:—

• (i) in which the relationship between the pressure loading and the integrals of the downwash over the wing surface is extended as far as possible, and which has to be computed numerically;

• (ii) in which approximations are made for the upwash velocities in the neighbourhood of the leading edge, resulting in a series of standard integrals for the estimation of the pressure loading.

Method (ii) is applied to the pressure loading on a flat plate triangular wing and cropped delta wing, and the application to more general shapes is discussed.