In the first 30 years of its existence, the helicopter has grown four times in speed and 75 times in gross weight. A comparable period in fixed-wing operation showed a speed growth of eight and 40 times in gross weight. The US aerospace industry (total 1.3 million persons) is currently employing 48 000 (3%) of its total force to build helicopters. However, this 3% is delivering over half of the manned aircraft being procured. US military inventory of helicopters has grown from 7317 helicopters in fiscal 1966 to 12 486 in fiscal 1969, thus comprising 35% of US manned aircraft. Military pilot training has already swung in favour of helicopters in the US, with 6000 fixed wing pilots trained annually compared with 7500 helicopter pilots annually. A similar trend is expected to take place in Europe and Asia.

The helicopter is beginning to stabilise in several fairly clear families or classes.

The Space Division of the North American Rockwell Corporation has developed a comprehensive computer-based heat transfer and thermal analysis capability especially for design support of the Apollo command module. The heat transfer analysis primarily centres about the solution of the diffusion equation using finite difference approximations. Since most problems encountered are non-linear in nature this approach has proved highly effective in producing accurate results economically. Recent studies, however, indicate that heat transfer problems are most successfully analysed by the finite element method. On the other hand, the finite element method in this field of application was not yet established when North American initiated this work. Lack of time does not allow a deserved discussion of this topic.

The purpose of this Report is to record the result of an independent step by step check of the theories, calculations and design proposals originated by Fit. Lt. Whittle, and having for their object the achievement of practical stratospheric transport. No investigation of the patent situation has been attempted.

The inventions and discoveries of Fit. Lt. Whittle have not yet reached the experimental stage, and so the material available for investigation is, necessarily, confined to a reasoned statement of the principles involved, coupled with justifying aerodynamic and thermodynamic calculations and design proposals.

The year 1909 was certainly the Golden Age of aviation in Europe, but another year was to pass before practical flight became a reality in England. In this country in 1909 not only was the need felt for an efficient aeroplane, but a good flying ground was also lacking. The year saw three brave attempts to establish such a ground, those of Noel Pemberton Billing at Fambridge, the Aero Club at Shellbeach and the Aeronautical Society at Dagenham. Only at Shellbeach did any flights take place, and all of the grounds were to be abandoned as unsuitable by the end of the year because of their rough terrain. Of Fambridge and Shellbeach some history has been recorded, albeit not enough, but Dagenham has been sadly neglected, even in the Society's own histories. This paper is an attempt to rectify this omission.

In ref. 1, an extension of the Kantorovich variational method of minimising a functional is discussed. The extension is based on an iterative technique wherein functions derived from the solution of sets of simultaneous ordinary differential equations are used again in cyclic order to obtain an improved solution. It is conjectured that if the iterative procedure is continued indefinitely, the functional will be close to its correct value, and so also will the associated function. The method given in ref. 1 is a generalisation of the iterative technique for minimising a double integral given by the writer in ref. 4, although in this work the iterations are carried out in the first approximation of the Kantorovich method and convergence is obtained in the usual manner of Kantorovich. Like ref. 4, ref. 1 uses the classical torsion problem of a rectangular bar as an illustrative example. Each shows that accurate Prst approximation solutions can be obtained and ref. 1 goes on to show that, for this particular problem, the derived functions are unique and are not dependent on the initial choice for part of the function.

The use of an expansive area change immediately following the diaphragm has afforded considerable convenience in shock tube applications and has been studied by a number of authors. It allows the use of a smaller diaphragm, thereby reducing the disturbance to the shock tube flow caused by the diaphragm opening, and it also permits greater flexibility in the choice of driver section configurations for a given shock tube size.

It is natural to consider the extension of this idea to shock tunnel operation. This has been encouraged by the possibility of applying area change to operation of an arc-driven shock-tunnel. Some early success in employing arc-heated drivers for shock tunnels has been reported by Warren et al. However, the configuration they studied employed a long driver section to achieve correspondingly long test times. In addition, to achieve a constant shock velocity it was necesssary that electrical energy was added so that the gas was heated uniformly before the diaphragm ruptured. This necessitated a fast discharge condenser bank, with a high discharge voltage, the latter to enable an arc to be sustained over the length of the driver section. In the present application, a constriction between the driver section and the shock tube is employed, allowing the driver section to be treated as a constant pressure reservoir of gas. It is anticipated that this will allow the use of shorter drivers, thereby permitting the adoption of lower discharge voltages, and will also allow energy to be added relatively slowly while the shock tunnel is operating. This will produce substantial economies in provision of the large energy storage facilities required for shock-tunnel operation.

The analysis of a cylindrical shell with cut-outs, which are reinforced to reduce the stress concentrations, is of importance in many engineering fields, particularly in aircraft structures. The most common assumptions made are that the curvature effect is negligible and that the reinforcement is a compact flexible bead. In the analysis of holes in fuselage shells the neglect of the effect of curvature may lead to serious errors as shown theoretically by Lurie and Vandyke and experimentally by Houghton and Rothwell. In some cases the bending stresses are of the same order as the membrane stresses which themselves may be much higher than the flat plate solution. Lurie obtained a perturbation solution for an unreinforced hole by expanding in powers of curvature parameter β, the results being valid for small values of β. Vandyke extended this solution up to β=4 by using a collocation procedure. In fact, if the collocation method is used it seems possible to obtain a convergent series solution for any β, the only limitations being the shallowness of the shell and the restriction that the deflections are not large.

The problem considered in the present note is that of the laminar boundary layer created by the motion of a strong shock wave. Such shock-induced boundary layers occur in shock tube flows behind the primary moving shock wave. For structural reasons, shock tubes frequently do not have very large diameters, so that such boundary layers often adversely affect the quality and duration of the test gas flow. The latter problem is studied, for example, in ref. 1 and to attempt such a problem a fairly detailed knowledge of the behaviour of shock-induced boundary layers is required. Such basic boundary-layer studies have been described in refs. 3-8 and the situation which occurs when the shock wave is strong is investigated here. The boundary-layer equations are expanded in a series form which involves a small parameter. This small parameter is shown to be the ratio of the gas densities fore and aft of a strong shock wave.

Several authors have considered the lifting characteristics of various simple shapes at hypersonic speeds. Non-weiler has dealt with shapes derived from wedge flows, and Townend has considered a class of two-dimensional shapes with concave undersurfaces. Cole and Aroesty and Pike have both considered two-dimensional shapes which are perturbations of simple wedge flow. They show that slightly higher values of the lift-to-drag ratio than that of the wedge are obtainable. Cole and Aroesty apply hypersonic small disturbance theory, under the constraint of constant lift, and suggest that the optimum shape is a “multi-wedge”. They show further that the optimum of a more restricted class of shapes having undersurfaces made of two plane surfaces, has a slightly concave surface. Pike has applied a more accurate (second-order) perturbation theory to a class of shapes which consist of small deviations from a wedge. He finds that the optimum undersurface consists of two plane surfaces, and confirms Cole and Aroesty's result that it must be slightly concave, except perhaps at low Mach numbers below the hypersonic range. It must be remembered that these results depend upon the assumed constraint of constant lift.

The problem of flexural vibration of a rotating cantilever blade is non-linear when the vibration takes place in a plane other than perpendicular to the plane of rotation. The non-linearity arises from the effects of Coriolis accelerations due to the rotation of the blade mounted on the periphery of a disc. Lo and Renbarger neglected the non-linear terms in their investigation and arrived at a simple relation for the frequency of vibration in terms of the stationary frequency of the beam, the rotating speed and the orientation of the plane of vibration. Lo in his analysis simplified the non-linear problem by assuming the blade to be rigid everywhere excepting at the root and presented the solution in a phase plane. Isakson and Eisley have considered a similar model to determine the natural frequencies in coupled bending and torsion of twisted rotating cantilever blades.

Part I (ref. 1) explained the ideas underlying Cheeseman's circulation-controlled rotor proposals and described the wind tunnel experiments on circular sections equipped with circulation control slots. The present paper describes the model rotor built and tested at the National Gas Turbine Establishment. Its hovering performance is fully analysed using the sectional performance correlation of Part I.