The free flexural vibrations of rectangular plates with various boundary conditions have been considered by Warburton. The natural frequencies were calculated by the Rayleigh method, the mode assumed being the product of the characteristic beam functions for the given boundary conditions. Comparison with experimental results shows that the method gives reasonably good approximations. The present note describes a method of obtaining the approximately equivalent characteristic beam functions to enable Warburton's method to be extended to plates having one or more stiffeners parallel to an edge. As a numerical example expressions for the frequencies are derived for a plate, simply supported along two opposite edges, and having a central stiffener parallel to the other two free edges. The results are compared with those given in a recent note by Kirk, who solved the same problem by the Rayleigh-Ritz method, using a mode with one arbitrary parameter. In the case of the fundamental frequency of the unstiffened plate, the characteristic beam function in a direction perpendicular to the free edges is simply a constant, and the solution is less accurate than that given by the Rayleigh-Ritz method. However, numerical analysis of a square plate shows that above a certain stiffener depth the characteristic beam function method is more accurate than the Rayleigh-Ritz method. The two methods are also compared for the 2/2 mode.

The Biot-Savart law gives the velocity associated with an elemental portion of line vortex, or the magnetic field associated with an elemental portion of line current. The following proof may appeal to students who approach fluid mechanics or electromagnetic-field theory from the engineering viewpoint. It will be stated in terms of fluid mechanics.

Consider a very small length δs of line vortex of circulation strength Γ. At P(x) the velocity δV associated with this portion depends on Γ δs and x.

Half a year has passed since the major airlines of the world, in a burst of energy, rallied round to “save” the Warsaw Convention. The Convention had as its principal effect a limitation of $8300 (not quite £3000) on liability of air carriers to international passengers for death or injury, and the United States had given formal notice that it could no longer accept this. The effort to update the Warsaw Convention of 1929 had, essentially, failed so far as the United States was concerned, in that the revision proposed at the Hague Conference in 1955 was only double, the Warsaw limit—$16 600 or £6000— still far below an acceptable ceiling on recoveries for accidental death caused by common carriers. The United States Senate had not ratified the Hague Protocol, it clearly was not going to, and all attempts by the United States Executive Branch to supplement the Warsaw/Hague limits—such as by compulsory trip insurance or voluntary waiver of limits by the carrier—had come to naught.

The feasibility of using neutrally-buoyant (or fully-buoyant) airships for passenger and cargo transportation is investigated. The drag coefficients of rigid and non-rigid airships are deduced from flight data. Comparisons are made with empirical drag formulas and previous wind tunnel data. Some general trends for airship drag are derived. The mass breakdown of non-rigid airships with hull volumes up to 35,000m3 is analysed using parametric equations. The maximum feasible airspeed and useful load carrying capacity of projected airships are calculated. ‘Specific productivity’ is found to be lower than values achievable with fixed-wing aircraft, but ‘fuel-specific productivity’ is found to be competitive, confirming results of a previous NASA study. The use of gaseous hydrogen and fuel cells is briefly discussed.

The purpose of this paper is to present a new approach in the concept and implementation of autonomy for autonomous spacecraft. The one true ‘artificial agent’ approach to autonomy requires the spacecraft to interact in a direct manner with the environment through the use of sensors and actuators. Rather than using complex world models, the spacecraft is allowed to exploit the dynamics of its environment for cues as to appropriate actions to take to achieve its mission goals. The particular artificial agent implementation used here has been inspired by studies of biological systems. The so-called ‘cue-deficit’ action selection algorithm considers the spacecraft to be a non-linear dynamical system with a number of observable states. Using optimal control theory a set of rules is derived which determine which of a finite repertoire of behaviours the spacecraft will perform. A simple model of a single imaging spacecraft in low polar Earth orbit is used to demonstrate the algorithm.

An exact analysis is made of reinforced sheets having three fibre directions using netting analysis. Load envelopes of shear combined with both uniaxial and biaxial tension are assumed and optimum fibre arrangements are determined on the assumption that limits exist on the compressive and tensile forces which may be developed in a fibre. Such optimum fibre arrangements are compared with the best-arranged isotropic reinforced sheets and with hypothetical solid sheets having the same properties as the fibres. Elastic constants are derived for the optimum systems. The total allowable load envelopes of the optimum arrangements are found and are related to the prescribed load envelopes.

It is commonly stated in the literature on laminar flow control (see, for example, ref. 1) that the important parameter controlling the height of tolerable roughness is the Reynolds number per foot, or unit Reynolds number, Vh; provided this parameter is the same in any two cases (which are closely geometrically similar) then it is assumed that the tolerable roughness height will also be similar. It is the object of the present note to point out that this is true only in very restricted circumstances and that in general the actual physical scale is also of considerable importance, as the following shows.

This paper is concerned with the effectiveness of reinforcing a hole in a plate on one surface only. The particular problem considered is that of a circular hole in a plate of infinite extent, subjected to axially symmetrical tension at infinity, when the reinforcement consists of an annular plate on one surface. Because of the interaction between bending and stretching, the problem is highly non-linear and it has only been possible to solve it for certain limiting cases. The stress concentration factor depends on a dimensionless parameter proportional to the tension at infinity. It is shown that the stress concentration factor is increased, because of the eccentricity of the reinforcement, if the parameter is small, but for values of the parameter greater than a certain minimum the stress concentration factor is decreased. The results also make it quite clear that there is no possibility of obtaining reasonably accurate results by linearisation of the equations.

The practice of using mathematical models to simulate pilot behaviour in one–axis stabilisation tasks is a well–known conventional simulation problem. In this paper an accepted mathematical model of a pilot is used as the controller of a rudimentary helicopter model. Flight test manoeuvre data from inverse simulation runs is used to provide time–histories which represent input forcing functions to the pilot–helicopter system, and a constrained optimisation routine is utilised to obtain values for the pilot gain and lead/lag equalisation parameters. It will be shown that as the theoretical pilot is required to ‘fly’ different manoeuvres, or indeed if the level of manoeuvre aggression is varied, the ‘pilot’ adjusts these parameters to perform a tracking task in compensatory control. The paper considers initially the pilot and helicopter models and subsequently analyses the whole system, illustrating how the pilot model changes with different situations.

The possible steady rates of roll of an aeroplane are determined in the case when inertia cross-coupling is present. This phenomenon not only changes the simple linear relationship between aileron angle and rate of roll, but may lead to more than one possible rate of roll for a given aileron angle. Simplified equations of motion are given for the cases in which the rolling takes place (a) from level flight, (b) during a pull-out manoeuvre. In both cases, these equations, which are non-linear, are solved numerically for typical examples. The static stability of the possible steady motions is considered in detail, and the dynamic stability is determined in the numerical examples.

A practical application of two-dimensional subsonic bluff body flow research can be seen in the design, construction and positioning of tall slender buildings. Similarly, from a three-dimensional viewpoint, drag reduction and vortex control is an important factor in the latest road vehicle designs. From just these two examples it can be seen that the problem of flow about a bluff body is one of major practical importance, while at the same time being of great theoretical interest. However, despite many years of extensive testing, there has been little progress made on the theoretical investigation of turbulent base flows since the foundations laid down by Kirchhoff and von Karman. The non-steady processes in the wake, in particular the complex dynamics of vortex formation, have proved to be problems of formidable size.

A stiffened shear web, consisting of a thin plate (referred to simply as the web) attached to longitudinal members (or flanges) and supported by a series of transverse stiffeners, buckles in a mode involving both the web and stiffeners, at a shear stress which also depends on the restraint between the web and flanges. With increasing stiffener size changes in the mode of buckling occur until, at a certain critical value of the flexural stiffness of the stiffener, buckling is largely confined to the web between stiffeners, and the buckling coefficient is then practically constant. The buckling coefficient reduces to that of an unstiffened flat plate with decreasing stiffener size.

Engineering Sciences Data Item 02.03.02 plots buckling coefficients for long shear webs with uniform, equally-spaced stiffeners. The curves are based on work by Stein and Fralich, for stiffeners of zero torsional rigidity and simply-supported longitudinal edges, and on a more recent series of papers by Cook and Rockey (listed in the Data Item) which extend the analysis to clamped, as well as simply-supported, webs and also include the torsional rigidity of the stiffeners.

Seven years ago a paper on this same subject was read before the Main Society. This has been used as a basis from which to start.

It will be seen that great strides have been made in performance, and the projects in the Design Office and on the drawing boards particularly, would even satisfy parliamentary critics. In Derby, however, where jet lift was conceived, such things are well known. From the fuel system standpoint in general the changes in requirements have been routine, merely much greater fuel demands, greater altitudes and air speeds and hence, a greater range of fuel flow, and it is this which gives the fuel system engineer his greatest worries. Beyond this there is always the need for smaller and lighter units in fancy shapes.

Sir Henry Tizard’s work and–above all–his part in our survival in 1940–have been the subject of many memoirs since his death in 1959. The biography written by Ronald Clark at the invitation of Professor J. P. M. Tizard, Sir Henry’s eldest son, will shortly appear. This first Memorial Lecture of the Royal Aeronautical Society thus occurs when a full record of Tizard’s life is about to be made available, and there is therefore little point in the plain re-iteration of a condensed biography. Future Memorial Lecturers, as they inevitably grow more remote from personal contact with Tizard, may well choose to describe the advances of the future in those fields to which Tizard himself so notably contributed: science, defence, education and government. My purpose in this first Memorial Lecture is, therefore, to build a bridge between biography and those future fields in which Tizard’s example, although unlikely to be excelled, will be emulated and extended.

The paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.

The possibility of sustained flight by heavier-than-air-machiaes was fully recognised during the last century by those who had studied the aerodynamic problems involved and it was realised that its accomplishment awaited only the development of a prime mover of sufficiently light weight.

Of all the known forms of prime mover, the internal combustion engine alone held out any promise of fulfilling the conditions necessary .for sustained flight, namely, light weight not only of the engine itself but also of the fuel it consumes. Early attempts had, however, been made to fly with steam, propulsion and it is of interest to note that the very remarkable and cleverly-designed steam plant employed by Sir Hiram Maxim in 1894 was actually very considerably lighter per h.p., even including the boiler and condenser, than the petrol engine used successfully some nine years later by the Wright Brothers.

The work described was undertaken under a Ministry of Supply Contract to investigate the fatigue strength of certain materials where the expected endurance in use was less than the range of values usually examined in fatigue testing.

The material was supplied in the form of a 6 ft. x 3 ft. x 1/4 in. sheet of aluminium alloy MG5.

Tensile test pieces having a parallel length one inch wide by 4 1/2 in. long were taken in both directions from two diagonally opposite corners of the sheet. Later, similar longitudinal test pieces were taken from areas near the other two corners.

The plane bending fatigue test pieces were of the form shown in Fig. 1 and were all cut in the longitudinal direction. The waisted test portion was polished on the edges, the original sheet surface being retained on the faces. Steel plates were clamped to the ends of the test pieces by bolts passing through the holes in order to localise the strain in the test portion as much as possible.