Previous work by R. T. Jones on the drag minimisation of elliptic wings is extended to the case of the slewed wing with thickness. These results are used to calculate lift/drag ratios of idealised configurations related to a supersonic transport aircraft. The values of lift/drag ratio and optimum slenderness ratio found are comparable with those calculated earlier in studies of delta-like plan forms.

A method is developed for calculating the pressure distribution at zero lift for a class of slender configurations consisting of a wing of delta type plan form combined with a body of revolution of the same overall length. Slender-body and slender-wing theory are combined to take into account the interference between the wing and the fuselage. An expression is found for the pressure at a general point on the wing or fuselage, although some numerical integration is still needed. This expression is simplified to obtain algebraic formulae for the pressure at the wing-fuselage junction and along the top of the fuselage. A further simplification is possible when the fuselage radius is small compared with the local wing semi-span. A particular example is considered consisting of a “Newby” wing with a parabolic fuselage; pressure distributions and drag curves are calculated.

By generalising earlier work, an approximate method is derived for calculating compressible laminar boundary layers with an unfavourable pressure gradient, with the wall temperature and Prandtl number arbitrary and some allowance made for the viscosity-temperature law. The method merely requires two quadratures and uses tables of universal functions. On the basis of this method it is suggested that when the wall is at uniform temperature the viscosity-temperature law should make little difference to the results, and that, when the wall temperature varies spatially by a factor of two, the use of a linear relationship may introduce errors of order 4 per cent in the momentum thickness. It is further suggested that the effects of Prandtl number differing from unity will increase as either the Mach number is increased or the wall is cooled. These general conclusions are borne out by detailed numerical calculations in a few selected cases.

Thin-walled tubes, in. in diameter, of three hard aluminium alloys and of mild steel have been tested in fatigue under three systems of alternating stresses while subjected to biaxial mean tensions imposed by means of internal pressure. In fatigue under direct or bending stresses the hoop tension in the walls of the aluminium alloy tubes did not seriously reduce the fatigue endurance, but it did markedly affect the mode and rate of crack propagation; cracks initially transverse to the tube axis tended to develop very rapidly in the axial direction. This tendency was present under both fluid and gas pressure, and under gas pressure the cracks propagated so fast that the test piece was often blown to pieces before the gas pressure fell by leakage through the cracks. The gradual taper in wall thickness along the fillets joining the test section to the enlarged ends offered no barrier to propagation of the axial cracks and the whole test piece, including its enlarged ends, was often shattered. Propagation of the axial cracks was preventible by sufficiently reducing the fillet radius, or by a ring glued on. Under alternating torsion, both endurance and mode of failure were affected by internal gas pressure. The initial fatigue crack, either circumferential or axial, often extended over a length comparable with the diameter of the tube, except under low ranges of shear stress when the crack length was sometimes very short. At each end the cracks forked in a characteristic manner and under moderate gas pressure the portions of tHe wall between the prongs of the fork were blown outwards. Under high pressure explosive failure and fragmentation often occurred. Mild steel under alternating torsion with internal gas pressure exhibited the same modes of failure, and two or more fatigue cracks were often formed simultaneously. Under high hoop tension, cracks propagated rapidly and one test piece, after two million cycles endurance, failed by exploding. However, no mild steel test piece was fragmented. A tentative explanation is offered of the reason why, in tubes of small diameter, rather short fatigue cracks may be expected to lead to fast fracture under the static loading. Attention is drawn to the inference that the initial fatigue crack itself must develop very quickly to considerable length.

This paper, which describes a photoelastic determination of the elastic stress concentration factors associated with shouldered shafts subjected to pure bending, forms the second part of an investigation initiated by the Structures Committee of the Royal Aeronautical Society. A general description of the manufacture of the models, the photoelastic technique employed to evaluate the s.c.f. and the results of the tests on shouldered shafts subjected to torsion have been given in Part I (Ref. 1).

An exact solution for the symmetrical buckling under uniform radial thrust is obtained for a thin circular plate having a particular type of thickness function for the cases in which the edge of the plate is either clamped or simply-supported. In both cases it is found that the critical thrust necessary to produce buckling can be increased from its value for the uniform circular plate of the same material and volume by concentrating material in the central region of the plate. For the clamped plate the increase is about 18 per cent and for the simply-supported plate about 29 per cent.

The distribution of total pressure, stagnation temperature and gas velocity is determined for the subsonic region of a supersonic jet emerging from a solid propellant rocket motor into air at rest. Measurements of Pitot pressures in the supersonic flow region have shown that the flow follows the axis of an inclined nozzle within the order of accuracy of the measurements. Nozzle cone angle, and probably the expansion ratio, affect the jet distribution significantly.

The effect of a subsonic mean flow on the organ-pipe type of vibration of the air in a duct of uniform area is calculated. The flow at entry to the duct is assumed to be at constant stagnation pressure, and a range of exit conditions is considered. It is found that the effect of the mean flow is to reduce the resonant frequencies by a factor of (1—M2) (where M is the Mach number in the duct) and to introduce damping of the vibration. Except when the duct is terminated by an efficient diffuser, this damping is rather large and it would require a powerful driving mechanism to produce large vibrations in the duct.

In this paper the way in which an inviscid incompressible fluid changes its total pressure is discussed. The basic equations are set out and it is shown that changes in total pressure are essentially associated with time variable flows. Simple examples are worked to illustrate this and finally application is made to single-stage flow machines, using a simple vortex representation.

The paper describes compression tests on eight thin-walled cylinders of 3 ft. diameter and 0·035 in. wall thickness made of aluminium alloy plate. The lengths of the cylinders were either 6 ft. or 9 ft. Three of the cylinders were tested under axial compression up to buckling failure, and the initial buckling load, failing load and mode of buckling were observed. A further three cylinders were similarly tested, but these cylinders were subjected to internal pressure before applying the compressive load. The internal pressure had a twofold strengthening effect on these cylinders. Firstly, it induced a tensile pre-stress along the axis of the cylinder and, secondly, it resulted in the value of the compressive stress at which buckling occurred being greater than the buckling stress value for the unpressurised cylinders. The six cylinders were tested in a manner which allowed the end face of each cylinder to rotate about a diametral axis. A parallel platen device was used in testing the last two cylinders (in an unpressurised condition) which restrained rotation of the end faces of the cylinders. These tests enabled the effect of end restraint to be studied, and also enabled measurements of load-carrying capacity at large axial deflections to be made. The initial buckling loads, failing loads and modes of buckling observed in the tests were compared with existing large deflection theory.

Theoretical reaction rate considerations normally require homogeneity of the mixture supply. An attempt—necessarily crude by reason of the analytical difficulties—is made here to cater for the case of non-uniform fuel distribution. Assuming a point-source injector in a parallel pipe, the “loss” in reaction rate is calculated for a limited number of specimen cases.

Characteristic equations are derived for thin circular shells, based on various approximations to the linear elastic theory of small deformations. By representing the deformation in a Fourier series in the circumferential direction, the roots of these equations are computed for a range of the significant parameters and compared.

Standard techniques of mass-transfer theory are used for the prediction of ablation rates; the thermodynamic and chemical-kinetic material properties are introduced by way of enthalpy-composition diagrams; the interface condition is given as the root of a single non-linear equation involving material properties. The paper treats both steady ablation and unsteady ablation, the latter by means of a quasi-steady assumption which confines transient effects to the solid phase.

Detailed comparisons are made with the methods of Sutton, Bethe and Adams, and Lees. The formulations of the paper are shown to be equivalent to, but more general than, those of the earlier authors; it is suggested that they are simpler as well. Some improvements over previous practice are recommended in connection with the calculation of the shear stress at the interface.

Results of a study of the accuracy attainable from various approaches to low aspect ratio wing deformational analyses are described. Seven model multi-web wings, representing a restricted range of sweep angles, aspect ratios and other geometric factors, were tested for deflection influence coefficients. Methods of matrix structural analysis and other techniques, involving numerous idealisations, were then applied in the prediction of the test data. This paper presents the experimental data. Subsequent papers will describe the analytical methods, the level of test-theory correspondence, and the merits and shortcomings of the theories studied.

A theoretical solution is presented for the problem of the clamped circular plate loaded in uniform compression. The solution employs a numerical method programmed for a digital computer. Instead of solving the classical von Kármán large deflection equations, a step-by-step integration of the elastic differential equations of equilibrium is carried out until suitable boundary conditions are attained. The method is an extension of one developed earlier to explain the behaviour of the simply-supported plate.

Previous theoretical work on mass transfer cooling is reviewed and it is shown that this may be complemented by similar solutions that occur when the velocity outside a two-dimensional boundary layer varies as some power of the distance from the front stagnation point. The case of stagnation point flow with constant wall temperature is investigated in some detail, under the assumption that the temperature differences are everywhere small compared with the absolute temperature. Calculations on an analogue computer, supplemented by an investigation of the asymptotic behaviour, are used to determine the boundary layer development and heat transfer rates when the coolant is hydrogen, helium, steam or carbon dioxide. It is found that, on a mass flow basis, hydrogen reduces the heat transfer rate most and that steam is the next most effective of the substances investigated.

The application of electrical analogue methods to the analysis of the extension and flexure of flat plates is reviewed and the difficulties encountered in the satisfaction of the various boundary conditions are discussed. A new method for treating certain boundary conditions and the operation of the electrical analogue is described. New experimental results for two cases which present great analytical difficulty, the flexure of a plate with a free edge and a plate supported on columns, are given.

A method is suggested for designing the shape of the plan form of an unwarped swept-back wing so as to control the magnitude of the singularity that occurs in the chordwise loading distribution at the leading edge. At a Mach number of unity it is possible to do this simply and directly by an approximate application of linearised lifting-surface theory. Details are given of three families of wing plan forms, of varying sweep and aspect ratio, in all of which the strength of the leading-edge singularity is held constant near the wing tips, behind the Mach line from the root trailing edge. The local chordwise load distributions have been calculated in detail for several of these wings and it is found that in all cases the loading curves become effectively independent of spanwise position over that part of the span for which the singularity is constant.

Calculations have been applied to a series of flexible plates (delta, gothic and ogee) to estimate their static aeroelastic behaviour. Assuming linear aerodynamics, the general tendencies of Part I are particularised. Assuming non-linear aerodynamics, it is shown that in general two positions of equilibrium are apparently possible at each speed. The stability of the models is not considered.

The photoelastic “stress freezing” technique has been employed to evaluate the elastic stress concentration factors associated with the fillet blend radius in a number of shouldered shafts. The full range of practical sizes of blend radius and depth of shoulder has been examined. Comprehensive results for the shaft subjected to torsion, pure bending and axial load are given in this (Part I) and in two subsequent papers (Parts II and III).

The accuracy of the graphs of stress concentration factors is better than six per cent. Comparison has been made with the existing theoretical and experimental results for each mode of loading. The results of an investigation into die limiting value of the stress concentration factor (for a particular shoulder radius) as the depth of the shoulder is increased to infinity are included in Part III.