The transfer matrix method of vibration analysis is widely used for the calculation of the natural frequencies of turbo-generator rotors, and of propeller blades, axial compressor blades, turbine blades, and helicopter rotors. A comprehensive account of the method has been given by Pestel and Leckie. The basis of the method is to deine a state vector, which gives all the generalised displacements and forces at a given cross-section of the system. The state vector at one cross-section is then related to the state vector at a neighbouring cross-section by means of a transfer matrix. It is found that, by a suitable choice of the order and signs of the elements of the state vector, the transfer matrix can in many cases be made symmetrical about the secondary diagonal; that is the diagonal running from the top right corner to the bottom left corner of the matrix and is also often called the “cross diagonal”.

The large displacement analysis of shells of arbitrary form is rightly considered to be a formidable undertaking. A purely analytical approach to the solution of such problems involving also initial buckling, post-buckling and secondary instability or snap-through is at the present state of knowledge impossible. However, with the advent of the matrix displacement method initiated in 1954 it became increasingly apparent that this method would prove in time the ideal tool for the solution of such complex structural phenomena. Nevertheless, all efforts in this direction were bedevilled until recently by the lack of suitable elements, satisfying all kinematic compatibility conditions. The major breakthrough came in this direction through the invention of the triangular shell element SHEBA, which admits an arbitrary variation of curvature. This again evolved from a natural extension of the plate element TUBA of TN 14. At the same time the SHEBA theory of ref. 1 was restricted to small displacements or linear behaviour. To generalise it to large displacements was not possible without an additional major conceptual progress. This was achieved within the Technical Notes 17 to 20, which introduced the idea of a local sub-element and showed how its geometrical stiffness could be used to deduce the geometrical stiffness of the complete element by a physically evident argument. The attentive reader will have noticed that the sub-element of an arbitrary beam in space discussed in ref. 3 is the obvious component block for our shell element. As a matter of fact, the technique is simply based on the representation of the SHEBA element by a grid of beam sub-elements running along the natural α, β, γ directions.

Three subjects have been selected for discussion in this paper, each of which has a major influence on aircraft design and operating economics. These subjects are airfield performance, noise and aircraft utilisation.

For an aircraft to have good operating economics it must be able to operate with a high load factor over a large percentage of the routes on which it is to be used. The permissible take-off or landing weight, and hence the payload, can be limited by any one of many airworthiness requirements. These include take-off distance and climb, landing distance and climb, and obstacle clearance in the vicinity of the airport.

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

It is quite true that MacMillan gave corrections for both the wall effect and the shear effect. I did not say that MacMillan gave no results for the wall effect but it appears, however, that Patel took notice of a correction which did not include the wall effect.

Thus Patel puts the effective centre of the pitot tube at a distance from the wall y=½Kd and by consideration of a model consisting of a linear sublayer, a transition zone and a fully turbulent region derives a value for K of 1·30 and values for the constants in the logarithmic law profile, A= 5·5 and B=5·45.

In the effort to develop a cheap power source for developing areas we have designed and constructed a 32-ft (9·75 m) diameter airscrew windmill. The airscrew designed by ourselves, incorporates the most recent aerodynamic theory. It comprises three blades manufactured under contract by a Canadian firm in fibre-glass reinforced epoxy resin. The manufacturing method is reasonably inexpensive and gives scope for local production in the developing countries at a later date. The shaft drive down the tower incorporates standard automobile and truck transmission components, which are available cheaply in many countries.

It is a well-known fact that buckling values for columns under dynamical loads are different from those under static loads. Meier, Gerard and Davidson have already investigated the dynamics of the buckling of elastic columns theoretically and experimentally, and Hoff discussed analytical methods in detail. However, solid viscosities are neglected in all these researches. Previously, the author obtained the relationships between dynamic load factors and solid viscosities, and it was found that their effects on dynamic load factors cannot be neglected. It will be interesting to investigate the relationships between solid viscosities and dynamic buckling values.

Operation of vehicles over dusty terrains and unprepared airstrips has highlighted the erosion problems incurred by ingestion of dusty air. Hibbert summarised the experience from British helicopter trials up to that date and drew attention to some of the factors that influenced the extent of erosion damage and to methods of minimising it. He cited a trial during 1963 in which a twin-engine Wessex Mk 2 helicopter having one intake protected by felt filters was tested in North Africa. Some idea of the severity of the problem may be gained from the fact that the unprotected engine surged after 3h 40 min while the other was found to have lost half its surge margin. However, operation can usually be arranged so that time spent in the dusty environment is minimised and service lives under desert conditions may be typically around 100h. In attempts to improve lives to a more acceptable level, different types of filtration have been investigated and the mechanism of erosion studied in some detail. This note describes some laboratory experiments to determine the influence of particle size on the erosion and attempts to relate this to filtration and engine life.

The rectilinear flow of an incompressible viscous fluid along a duct of uniform cross section due to an oscillating pressure gradient has been considered by a number of investigators. The duct of circular cross .section has been treated by Richardson and Tyler and Sexl, the elliptic case by Khamrui, and the rectangular case by Drake and Fan and Chao. Recently Jeng has discussed the importance of this type of flow and has given a procedure for calculating a numerical solution for a duct of arbitrary cross-section. An interesting feature of these flows is that, at large frequencies when the flow is of boundary-layer type, the velocity at any instant has its maximum near the walls, the velocity overshooting its almost uniform distribution at the centre of the duct.