An attempt is made to assess the rate at which failures occur within a group of similar structures, or structural components, when each structure is subjected to the same set of applied loads. The structures are similar in every respect except for small inherent differences in strength from one structure to another. On infrequent occasions the applied loads may be so intense as to destroy the weaker members of the group. For the problem in which the structural strengths are distributed within the group in a “normal” fashion, and when the frequency of severe loads diminishes exponentially, it is found that the rate at which failures occur within the group of structures is governed by two simple non-dimensional parameters. Numerical values of these parameters are studied more fully.

A study of the laminar boundary layer on a yawed infinite wing in a compressible fluid is made. A method is presented for the investigation of compressibility effects by direct solution of the linearised equations of motion, first considerably simplified by the extension of a transformation due to Illingworth and Stewartson, which assumes a heat-insulated surface and a fluid of unit Prandtl number and a coefficient of viscosity which is proportional to the absolute temperature. As an example of this procedure the boundary layer near a stagnation point is calculated. The simplifications necessary for an extension of the momentum method, which is available for a yawed infinite wing in an incompressible fluid, are discussed, and this method is recommended for a first evaluation of the effect of compressibility.

The paper discusses the influence of wire length on the characteristics of a turbulent flow as measured with a hot-wire anemometer. Most of the mathematical treatment can be directly applied to other problems of length correction, such as may occur, for instance, in problems of astrophysical turbulence, as well as to some problems related to measurements of random processes. The discussion will, however, use the example of a hot-wire anemometer with particular attention to the influence of the length of the wire on the measurement of the intensity of turbulence, correlation coefficients, and scale and microscale of turbulence.

The distribution of pressure over a lifting surface in subsonic potential flow is investigated by means of a three-dimensional electrical potential analyser. It is shown that by using the linear perturbation theory it is possible to obtain the pressure distribution for small angles of incidence, as well as the slope of the lift-incidence curve, easily and rapidly. A comparison with results obtained by vortex theory calculation shows a good agreement in spite of the relatively coarse network which was used for the experiments. There are no practical limitations to the use of a network having a finer mesh, and problems concerning curved and twisted surfaces may also be studied with facility by the use of the potential analyser.

The problem considered is that of the buckling of a right-angled isosceles triangular plate subjected to shear along the two perpendicular edges together with uniform compression in all directions. Four combinations of boundary conditions are considered, and the buckle is assumed to be symmetrical about the bisector of the right angle. In each case it is shown that, if the plate is subjected to shear only, the critical stress is changed considerably upon reversal of the shear. The larger value occurs when the shear is tending to decrease the right angle. Because of this fact, the interaction curve, giving critical combinations of compression and shear, is unsymmetrical and the critical compressive stress can be appreciably increased by the application of a suitable amount of shear.

In this paper the Janzen-Rayleigh method is used to calculate the velocity potential for the steady subsonic flow of a compressible, inviscid fluid past a prolate spheroid. The fluid velocity at a point on the body is calculated. The analytic form obtained for this velocity differs, from that giving the velocity which an incompressible fluid would possess at the same point on the body, by a correction factor. The factor is an infinite series of first derivatives of Legendre functions of the first kind and odd order. The first three coefficients in this series are computed for bodies of certain axis ratios, and graphs of the values of these coefficients against axis ratio are plotted. The behaviour of the nth coefficient for large values of n is given. Results for slender ellipsoids, considering these as a limiting case of the family of ellipsoids just referred to, are obtained and are found to agree with the usual slender-body theory. Using these an attempt is made to continue the graphs of the first three coefficients in the correction factor series for the whole range of axis ratios of the ellipsoids in the system, namely zero to unity. The results obtained for the bluff-nosed ellipsoids may be used to estimate the effects of compressibility on the pressure distribution over the front of a general bluff-nosed body in steady flow.

An old numerical method of solving fourth order differential equations is put in relaxation form. The higher order correction terms are included and the technique is illustrated by an example. The method has the advantage of being more rapidly convergent than the usual relaxation procedure for fourth order equations. Some comments are made on the numerical solution of the viscous flow equation.

A simple one parametric method, due to A. Walz and based on the momentum and energy equations, for calculating approximately laminar boundary layers is extended to cover axi-symmetric flow as well as plane flow. The necessary computing work is reduced a little.

Another known method which requires still less computing work is also extended for axi-symmetric flow and, with the amendment of a numerical constant, proves adequate for practical purposes.

The natural frequency of vibration of curved rectangular plates, with both simply-supported and fixed edges, is evaluated for the fundamental extensional mode. This mode is thought to be applicable when the plates are excited by a uniformly distributed pressure as may occur with a dynamic pressure wave. The natural frequencies corresponding to this mode increase fairly rapidly with the curvature of the plate.

The natural frequency of vibration of the plates when the mode is the fundamental inextensional mode is also considered. The frequency of this mode is higher than that of the extensional mode for small curvatures, but the inextensional mode frequency falls slowly with increase in curvature of the plate. Thus, if the curvature of the plate is sufficiently large, the frequency of the fundamental inextensional mode is lower than that of the extensional mode.

For supersonic wings it is known that the presence of a tip reduces the lift and the performance compared with the corresponding values for the two-dimensional wing. It appeared from some work by K. Stewartson that the addition of a vane at the wing tip might counteract this effect. The purpose of this paper is to determine the effect due to the presence of the vane. For this purpose a wing in the form of a semi-infinite wedge whose leading edge is swept back is supposed placed at incidence to the flow, with a symmetric triangular vane with diamond-shaped base attached to it, its vertex being at the tip of the leading edge, and its plane of symmetry parallel to the flow. The problem is of the “conical field” type and is solved by the method of S. Goldstein and G. N. Ward.

The problem is divided into its anti-symmetrical and symmetrical parts. The results obtained in Ref. 1 are applied to determine the field in each case, both outside and inside the Mach cone of the vertex.

A number of authors (e.g., Refs. 1 and 2) have dealt with the problem of uniform two-dimensional supersonic flow past a thin oscillating aerofoil, whose angle of incidence to the main stream is small. In this special case, the effects of vorticity are negligible, while the fields of flow on either side of the aerofoil may be treated on the same footing.

The object of this paper is to deal with the more general case in which the aerofoil performs small oscillations about a fixed position, in which its incidence to the main stream is appreciable.

In a previous paper the author derived, by the Rayleigh-Ritz method, a determinantal equation for obtaining the critical magnitude of any uniform system of edge stress applied to a clamped oblique plate. In the present paper this equation is used to derive values for the buckling stresses of clamped oblique plates subjected to pure shear along and perpendicular to two edges of the plate.

As would be expected, it is found that reversal of the direction of the shear produces a change in the critical value. The lower value occurs when the shear is tending to increase the obliquity of the plate and critical values corresponding to this direction are calculated for 45° oblique plates with side ratios varying between 3/5 and 5/3. The critical values obtained for the reverse direction were obviously very inaccurate, due to the inadequacy of the series which was used to represent the buckling mode. As yet no satisfactory method has been found for overcoming this difficulty.

The effects of distortion on the longitudinal stability of swept wing aircraft at high speeds (sub-critical Mach numbers) are considered on a quasi-static basis. The method is based on the theory of Gates and Lyon but involves some extension of this theory.

The treatment of wing distortion is considered in some detail and the effects of built-in twist and camber and wing weight are included, using the so-called superposition method. The application of the analysis of Lyon and Ripley for investigating fuselage, tail and control circuit distortion is suggested, but means of modifying and simplifying this procedure where desirable are put forward.

The analysis is illustrated by means of a simple example of a swept wing fighter aircraft for which wing, fuselage and tail distortion effects are considered, and the results are discussed with reference to the individual and combined distortion effects, as well as the effect of compressibility.

To calculate tail loads in flight it is necessary to know the angle of downwash at all points of the tailplane for any given value of wing incidence. Current trends in aircraft design place the tailplane off the plane of the wing. There exist solutions for the downwash in the z=0 plane for a delta wing with subsonic leading edges. This note gives a form of integral suitable for numerical evaluation which determines the downwash in the plane of symmetry (y=0) of a delta wing with subsonic leading edges. This note also points out an apparent error in Ref. 4 by G. N. Ward and gives a closed form for the downwash at a point whose forward Mach cone totally includes an arrowhead wing with supersonic trailing edges and whose centre line coincides with the axis of the cone.

The first object of this paper is to show the concordance between three different theoretical approaches to flame stabilisation and to compare published experimental data with the theoretical predictions. Good agreement between the theory and experimental results is obtained. The second object is to show that, at low pressures, the predictions of these theories must be qualified in view of the increasing importance of heat losses from the flame region. It is shown that there must exist a minimum pressure below which a flame cannot be maintained in a given combustible mixture, irrespective of the rate of flow of the mixture, unless heat losses are entirely eliminated.

A method is developed for designing thin finite wings with prescribed lift distributions. Particular attention is given to wings which, at a certain optimum angle of incidence, have zero loading along the whole leading edge. It is suggested that such a wing will have a greater range of lift coefficient for low drag than other wings with the same plan form.

On the basis of the linearised theory a formula, relating the wing surface to the pressure distribution over the surface, is deduced which differs from the usual potential relationship by avoiding the difficulty of the non-uniform convergence with respect to the normal distance away from the wing surface singularities. The surface integral which is developed includes a regular singularity and a definite limiting process.

The problem of a uniformly accelerated slender supersonic aerofoil is solved in this paper by a perturbation method for the cases when the acceleration is small. Full account is taken of the effect of the acceleration on the form of the shock line.

A generalised conical field theory is developed and is applied to delta wings in a non-uniform stream. It is shown that a non-uniform stream may be characterised by the downwash at all points in space. The lift of a delta wing is found when the downwash in the wing plane is given as a power series in the co-ordinates in the wing plane. The basis of the conical field theory is described in some detail but the results only of the calculation of the lift distribution for various down washes are given. The solutions of certain integral equations, required in the calculations, are given in the Appendix.

A simple method is developed for computing the trailing vorticity which arises when a non-uniform stream is turned.

It is shown that, for a sudden and constant deflection of a non-uniform stream, no net trailing vorticity is set up in the exit flow and hence there is no secondary motion.

In the case of an impulse cascade of finite dimensions with constant turning, it is found that the trailing vorticity has three distinct components—the passage vorticity and two components which appear as vortex sheets springing from the trailing edges of the aerofoils. It is shown that for small angles of deflection there is no net circulation associated with the trailing vorticity downstream, of the cascade, and it is inferred that this should still be so for large deflections.