Lagrange's Interpolation formula can be used to obtain an approximate polynomial representation of a curve (derived empirically, or known otherwise) as well as to interpolate between isolated values of a function. In obtaining such an approximating polynomial, standardisation of the values of the independent variable has the advantage that many relevant quantities can be calculated and tabulated (or plotted, or both) in advance.

Early in 1950 it was decided to modify experimentally the original jet–driven tunnel of the English Electric Company—Aircraft Division, from a subsonic to a transonic tunnel. This was inspired by the work of Ward and Wright at Langley Field. As little was known then of the pressure ratio to operate a transonic working section, the working section area was reduced from a 3 8 square foot subsonic section which could be choked, to one square foot. The working section and diffuser for this modification were quickly manufactured from wood. In addition to the new working section and diffuser, a steel fairing was added to reduce the cross sectional area of the mixing length and so match the smaller induced mass flow.

The use of models in the determination of aircraft behaviour is as old as flying itself, and wind tunnel models in particular have played a very important part. Now that supersonic flight of aircraft and missiles is a matter of common experience, it seems appropriate to look at some of the difficulties involved in the supersonic tunnel testing of models of such machines.

In recent years, due to the high cost of continuous supersonic wind tunnels, much attention has been focused on the simpler intermittent “blow-down” tunnel.

Considerable data has been published on most aspects of the design of this type of equipment and quite a number of large installations have recently been brought into operation in the United States, with even larger numbers currently building both in this country and in the United States.

Workers in the field of continuous combustion have long been aware of the importance of the part played by the aerodynamic factors in the satisfactory operation of combustion systems. Although only part of a complex process, the air flow in a combustion system can, to some extent, be studied as an isolated individual factor, without the complications of fuel injection and heat release. This may appear to involve a rather long step from reality, but observations of the basic “cold” flow conditions in such a system can provide a valuable basis for the prediction of the effects of variations in the equipment, particularly in systems conforming to a particular type.

The Ordinary convergent exhaust nozzle is a perfectly satisfactory and efficient device for converting pressure in the jet pipe into velocity, so long as the pressure ratio across it remains below about 2.0; or, put another way, so long as the velocity at exit from the nozzle is not theoretically greater than that of sound at the jet temperature prevailing. If the pressure ratio is greater than this however, full expansion cannot take place and some losses in thrust occur. The pressure ratio across a jet pipe on modern jet engines is of the order of on the test bed, so already under these conditions some losses occur. The amount is insignificant however, but in flight at supersonic speeds the pressure ratio across the jet pipe may become very large, and in this case important losses result.

A method for providing lateral control at supersonic speeds by means of control surfaces located on nacelles or on the fuselage is described. These surfaces are arranged so that they affect the pressures over adjacent wings, and hence produce a rolling moment. The note includes the results of calculations and of a limited number of measurements which enable the effectiveness of such controls to be estimated.

The difficulties of determining latitude and longitude under adverse weather conditions, when neither the Sun nor stars can be sighted, are well-known, and the advantages of a non-visual system of position finding which could operate through clouds or fog are too obvious to require emphasis.

A Radio Sextant, which detects and locks-on to 8 mm. radiation from the Sun, has already been made and tested in America with reputedly excellent results. An analysis of both the theoretical and the practical design factors is given in the present paper, together with the results of successful experiments made in Great Britain.

Slender Struts are usually tested with pin joints at both ends, because this is the theoretical condition which is most readily achieved (or closely approximated to) in practice. In conventional testing machines this results in a compression column with two pin joints. The instability of this column makes the accurate alignment of the loading members important, and reliable testing becomes correspondingly difficult.

We are now, I believe, at a time of crisis in aeronautics and in Great Britain the sense of crisis is made more acute on account of the issue by the Government of the White Paper on Defence for 1957. This paper announces vitally important changes of Government policy which are intimately concerned with aeronautics. For example, the policy is to make the English Electric P.l Supersonic Fighter the last of the manned fighter aircraft in Britain and to concentrate effort in defensive aircraft upon the unmanned guided weapon.

The so-called ejector nozzle has received a large amount of experimental study as a means for achieving efficient supersonic expansion of the main jet without the difficulties of a mechanically variable convergentdivergent nozzle. No satisfactory theory for the calculation of its performance has yet been put forward and it is the object of this paper partly to remedy this defect.

Before enlarging on the main subject of this paper, it will be helpful to clarify some fundamental conceptions of various rotor drive configurations.

In the past the original shaft-driven helicopter presented two major problems to the designer. These were first: the necessity to choose between either some torque balancing device or a multi-rotor layout and, second: the necessity of a large reduction gear box, the weight of which seemed to become prohibitive with increasing all-up weight of the design. Big helicopters with either single rotor/tail rotor configuration or multi-rotor configuration, are flying successfully and prove that these afore-mentioned problems, although still in existence, were mastered in an admirable way. Nevertheless, in the old days the words “ tip. drive ” had a magic sound to the harassed designer.

Several methods are available for the solution of problems of forced vibration of systems with nonlinear elastic characteristics. Of these, the Martienssen, Den Hartog and Rauscher methods may be applied even if the restoring force characteristic is only known graphically, while the Duffing and Perturbation methods are only applicable when the restoring force characteristic is expressed in a convenient mathematical form. Successive approximations are used in the Duffing, Perturbation and Rauscher methods and therefore any desired degree of accuracy can be obtained. The Den Hartog and Martienssen methods give a two-term and one-term solution respectively.

An Adoption of matrix techniques is proposed as a method for the solution of torsional natural frequencies in a branch or geared shaft system. Both fundamental and higher mode shapes and frequencies are produced by a comparatively rapid and straightforward technique. The method is illustrated by a numerical example of a coupled turbine and reciprocating engine system driving a common propeller.

The Propelling Nozzles tested are turned from brass and the interior surface finish shows a centre line average of about 15 micro inches when examined on a Taylor Hobson machine. This is fairly rough compared with the estimated boundary layer thickness and it was required to know whether this in fact affected the thrust. The thrust of a nozzle manufactured by the usual process was measured before and after a polishing process. An improvement of one half per cent was recorded.

The subject of this paper is a wide one. Guided weapon development problems in one form or another have been my daily concern for more than ten years now and I must be highly selective in the brief time at my disposal on this occasion.

The object of guided missile development is to produce efficient weapons of war, that is, weapons of destruction able to neutralise an enemy threat or destroy the enemy if he dare attack. I make this statement every time I talk on guided weapons, and I make no apology for making it on this occasion. We must not at any time forget that we are concerned in the development of weapons to defend this country, that time is of the essence of the contract, that the product must stand up to storage, to usage by the Services, and must be ready for action after little warning, and so on. As in any other branch of engineering, we have to make the best use of the men, ideas, techniques and materials at our disposal in order to reach the desired objective.

The development of wind tunnel sections with partly open walls has made it possible to operate at continuously variable speeds through the transonic range up to low supersonic speeds. Some consideration must be given, however, to the general reliability of the measurements in these tunnels of the aerodynamic characteristics of air vehicles or missiles. A comparative assessment of the possible overall errors in force and pressure measurements in relation to desirable standards of accuracy is, in fact, required. A number of points connected with such an assessment are briefly discussed (mainly on the basis of experience in the 3 ft. tunnel at R.A.E., Bedford) in this paper, which touches on flow uniformity, accuracy of model manufacture, and interference effects, including a comparison between tunnel and free flight model results; illustrative examples of results for an aircraft model, with some full scale flight comparisons, are discussed briefly and a few comments are made on the problems associated with the achievement of representative flow conditions on sting–mounted models at transonic speeds.

A Method is presented for determining approximately the effects of small changes in the characteristics of a dynamical system on its free motion. Successive factorisations of the determinantal equation, as the system is altered, are avoided at the expense of accuracy, but the influence of the small changes on, for example, the stability of the system, are quite easily determined.

Around the end of the fifteenth century were written what must have been about the first set of airworthiness requirements ever compiled. These were notebooks of Leonardo da Vinci in which he discussed the physics of flight and the design of flying machines. In one of these notebooks he wrote:—

“ In constructing wings one should make one cord to bear the strain and a looser one in the same position so that if the one breaks under the strain the other is in position to serve the same function.”