Simple Formulae are presented for the first three bending-type and the first torsion-type natural frequencies of any constant thickness cantilever triangular plate. The formulae are derived by a semi-empirical method. Comparison of calculated frequencies with test values indicates agreement within a few per cent. for a variety of plate plan forms.

During the past hundred years much data on the fatigue behaviour of a wide range of materials has been accumulated and it is now well known, as a result of service failures and laboratory tests, that stress concentrators whether mechanically formed or inherent in the material, can cause serious reductions in endurance.

The work described in this note forms part of a project being conducted at the Aeronautical Research Laboratories, Melbourne, Australia on the effect of stress concentrations on the fatigue properties of materials. The primary aim of the project is to establish a series of fatigue curves for different materials under a wide range of theoretical stress concentration factors and to attempt to find a basis on which to assess the notch sensitivity of different materials. The first investigation was carried out on 24S-T aluminium alloy and tests on two additional aluminium alloys, annealed copper and an alloy steel are in progress.

The supersonic and subsonic jets are both considered by the method used by Miles for an oscillating aerofoil between wind tunnel walls.

The present problem and that of Miles are special cases of the flow past an oscillating aerofoil between porous walls, and provide a useful check for results in the porous wall problem. It may be assumed that the ratio of the change in pressure across a porous wall to the normal velocity at the wall defines a quantity called the porosity parameter, which is a constant at any particular point on the wall. For the special cases of the porosity parameter being everywhere infinite and zero, the porous wall corresponds to the solid wall and the free jet boundary respectively.

A simple set of curves is presented from which may be calculated the lowest natural frequency of flexural vibration of practically any triangular plate of constant thickness and with simply-supported edges. In many cases the results are self checking since the calculations usually may be carried out in three independent ways and compared.

A method is given whereby the shear stress-strain relationship of a material can be obtained from observations made during a torsion test on a hollow circular specimen. An examination is then made of the corrections necessary when using thin-walled specimens, and some advantageous definitions of the mean diameter of a tube are suggested.

The use of torsion tests to obtain shear stress-strain relationships is now well established and takes one of two forms. A thin circular tube can be used, it being assumed that the stress distribution is uniform across the wall thickness, or a solid circular bar can be used, the results being analysed by a method ascribed to Nadai. Swift has shown that these two methods give comparable results for moderate strains.

The Society's All-Day Discussion on Aircraft Design Philosophy was extremely well supported and at one stage there were more than 350 members and visitors present. As is inevitable on these occasions there was insufficient time available for all those who wished to make a contribution to do so, even though the four lecturers had reduced their contributions to a bare minimum by presenting summarised versions of their papers.

With such an all-embracing title as Aircraft Design Philosophy it was obvious that some main channel of exploration would have to be chosen; that which evolved during the planning of this event was structural safety, as will be apparent from the discussion. The preparation of a summary of discussions presents a number of problems.

This note describes an investigation of experimental and theoretical data on the lift increment due to the deflection of full and part span controls. For full span controls, existing Data Sheets in the Royal Aeronautical Society Aerodynamics series are found to be inadequate for some of the plan forms currently in use, but the investigation shows that with one additional set of curves the sheets may be applied to almost any plan form. For part span conversion factors, a revision also is proposed.

The results are presented of an investigation of a particular type of baffle for the production of symmetrical velocity profiles having high ratios of maximum to mean velocity in ducted incompressible flow. Two similar families of profiles are obtained depending on whether a short (12 diameters) or a long (48 diameters) entry length is used before the baffle. The highest value of the maximum to mean velocity ratio obtained is 1·42 and the pressure loss coefficients associated with the use of the baffle are given together with an indication of the effect of Reynolds number.

It is shown that the flow in a region of recirculation may be divided into a core, in which the vorticity may be constant, and a boundary layer surrounding the core. An approximate solution is given for the flow inside a circular cylinder with partly fixed and partly moving walls.

Flow patterns which include regions of recirculation occur frequently, for example, behind bluff bodies, in sharp bends, and in sudden expansions in ducts. Little is known about this type of flow, which will be referred to, for brevity, as ‘cavity’ flow. It used to be thought that the velocities in the ‘ cavity ’ were small compared with the stream velocity, but it is now known that the maximum velocity in the cavity may be about 30 per cent. of the stream velocity. This implies that the motion within the cavity cannot be neglected.

The introduction of rational performance requirements governing the operation of civil transport aircraft has given rise to a need for accurate and detailed information on obstructions in the vicinity of aerodromes. This paper states the origin and nature of the requirement and describes a survey technique, a particular application of terrestrial photogrammetry, which was used to meet it.

In the United Kingdom and in other member countries of the International Civil Aviation Organisation considerable progress has been made towards the rationalisation of performance requirements governing the operation of civil transport aircraft.

In Switzerland aircraft often have to take off and land in narrow mountain valleys where a strong, irregular wind is blowing. In these circumstances one faulty casting may cause failure of a control; or a small part, if insufficiently heat-treated, may fracture and result in the loss of the aircraft. For this reason, thorough inspection during production and careful maintenance of the aircraft are of prime importance. Control within the aircraft factory consists of inspection of the raw materials, such as bars, sheet metal, tubes, castings, forgings and so on; testing of the most important parts during manufacture to detect cracks and to control the heat treatment; and the final control of all parts, of components and of the whole aircraft. Maintenance inspection reveals cracks, corrosion and other defects of the most important parts of the aircraft.

The compressible laminar boundary layer on a yawed infinite wing is considered in Ref. 1, where it is shown that the problem may be solved by a direct solution of the linearised equations of motion under certain assumptions. As an example of this procedure the boundary layer near a stagnation point was calculated. Tinkler has published solutions of the exact equations for the general Falkner-Skan case (Ref. 1) obtained on the M.I.T. differential analyser for several values of the parameter involved. It has been found that the numerical results of Ref. 1 were in error and the corrected results obtained by a new method are tabulated below. Tinkler's exact solution of the stagnation point flow for ω = 0·10 is also given for comparison, and it will be seen that there is close agreement

This note is presented as an idea to be criticised rather than as a description of a fully developed experimental technique. There are weaknesses in the method which will prevent it from giving absolutely correct answers, for example, the twist imparted to the boundary layer when a body of revolution is rolled cannot be represented. But some of the major effects can be represented, and the idea may possibly be developed to be of practical significance.

It is standard wind tunnel practice to measure the aerodynamic derivatives CYβ, C1β, Cnβ, CMβ, CLβ and CDβ by having a wind stream of constant direction, and measuring aerodynamic forces and moments on a model aircraft placed at angles of yaw and pitch to the stream.

Each small stage of the expansion starts with a uniform supersonic stream and finishes with a similar stream accelerated, expanded and turned through a small angle. We are therefore justified in applying to each stage the linear (Ackeret) approximation for small departures from uniform flow, according to which

where U = air velocity

M = Mach number

α = inclination of flow.

If the definition that hysteretic damping is proportional to displacement but in phase with velocity be accepted, then the free vibration of a simple oscillator may be treated, without ambiguity, using this concept. The apparent anomaly which Dr. Bishop points out in his paper “ The Treatment of Damping Forces in Vibration Theory ” (November 1955 Journal) arises through confusing three distinct possible mathematical representations of some unspecified vibrating system.

A simple and convenient “ endurance chart” for the presentation of basic fatigue data is described, where static failure is regarded as simply fatigue failure in one cycle of loading.

This chart shows the effects of mean stress, residual stress and pre-tension, and displays several interesting features of fatigue data. It is easily constructed directly from fatigue test results, and is very well suited to the calculation of stress concentration effects, including “ plastic relief ” effects.

With the aid of such charts the relative fatigue strengths and structural efficiencies of different materials may be readily compared, and it is clearly shown that in certain circumstances a “ high-strength” alloy may in fact have considerably less fatigue strength than a “ medium-strength ” alloy at a given life, or conversely a lower life at a given stress level.

It is demonstrated that the fatigue life of a component subjected to combined mean stress and alternating stress may be found only with a knowledge of the complete fatigue characteristics of the material (such as are presented in the endurance chart); and that attempts to estimate fatigue life from spot-value comparisons, such as the fatigue strength at an arbitrary given endurance, can be dangerously inaccurate. A chart of the form described thus forms a valuable step towards the accurate calculation of fatigue life.

The method is illustrated by the provision of endurance charts for 14S-T (L.65), 75S-T, and D.T.D.683; and with experimental results for notched components of L.65 and D.T.D.683.

An example illustrates the application of the chart to the calculation of the fatigue life for the case of two independent systems of loading acting on a pressure cabin with circular window cut-outs.

A method is given for finding the reciprocal of a matrix which is triply partitioned horizontally and vertically in such a manner that the sub-matrices in the principal diagonal are square, but these matrices need not be of the same order. A preliminary rearrangement of the matrix may be helpful.

In theoretical work it is sometimes required to find the reciprocal of a matrix which can be so partitioned that some of the sub-matrices are of simple types, e.g. triangular or nul matrices, and the calculation of the reciprocal may then be facilitated by using formulae for the inversion of partitioned matrices. The same method will be often advantageous in numerical work also. In an earlier paper the reciprocation of doubly-partitioned matrices was treated in a general way and a method was given for triply-partitioned matrices subject to the restriction that the sub-matrices in the principal diagonal are square and of the same order.