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; Part I gave experimental data. This paper describes, applies, and compares certain elementary and plate bending theories. A subsequent paper will deal with discrete element idealisations commonly employed in matrix structural analysis.

The benefit to be obtained by using an interference fit between the pin and plate in a pin-jointed connection has already been established. An examination of the published results shows that some non-linearity occurs in the mechanism of load transference from the pin to the plate since, except at very high initial interference, doubling the load on the joint more than doubles the maximum shear stress in the plate. An examination of the stress-load relationship shows a distinct discontinuity, the load at which this discontinuity occurs being dependent upon both the initial interference and the coefficient of friction between the pin and the plate. It is shown that the results hitherto published correspond to a coefficient of friction between the pin and the plate of 0.3 and results for lower and higher coefficients are given.

A semi-empirical analysis of unstable crack propagation in thin sheets is given. An effective value of the crack tip strain concentration factor is used as the criterion for instability. Good correlation is achieved with experimental results from unreinforced sheets of aluminium and titanium alloys and high-strength steels. The interdependence of geometry and stressstrain curve properties in determining the unstable crack propagation characteristics of sheet materials is illustrated in an appendix.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

By consideration of a series of simple models the static aeroelasticity of conventional aircraft is first discussed and then extended to the integrated configuration combining fuselage, wing and tail. It is shown that, on the basis of linear aerodynamics, a maximum speed exists at which control is possible. Overall deformations and control forces become large at speeds approaching this critical condition. Part II, to be published, contains calculations on slender plate aircraft including non-linear aerodynamics.

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.

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.

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.