I would first like to pay tribute to the inspiration which suggested the series of papers on The Next Hundred Years, the second century of the RAeS. John E. Allen's introductory paper in the January, 1968 issue of the Journal set the stage for a remarkable series of individual papers in which technology, philosophy and sociology have combined to give a vision of a challenging future, often exciting but occasionally sobering. Coming at the conclusion of this series, I have interpreted my task to be that of looking at this future through the eyes of a technical man in the aerospace industry of the United States. Before settling down to this task, it seems appropriate to make a few remarks on the general nature of technological prophesies; in doing so, I am following a pattern which has been set by a number of my predecessors in this series. Occasionally these general remarks have taken the form of a reminder of the uncertainty of the process of technical forecasting.

At the outset, may I emphasise how honoured I feel to be invited to speak before the Royal Aeronautical Society and that I am very grateful for the opportunity to give a report on the work and activities of the Dornier concern.

It is hardly possible within the narrow scope of a lecture to include any exhaustive and detailed discussion of the development and research work accomplished by the Dornier concern in post-war years.

Instead, I shall try to give you an idea of some of the work performed or still under way, which may perhaps reveal characteristics which are typical of our working conditions and methods.

In the past few years, many different VTOL experimental aircraft have been developed and tested in Europe, the USA and Russia and a great deal of experience has been gained.

Dornier's contribution in this field is the development and testing of the Do 31 VTOL jet transport (Fig. 1). A V/STOL aircraft concept had to be found, uniting the main advantages of relatively high flight speed, high pay-load capacity, operational flexibility, low maintenance requirements and great safety in case of engine failure. The Do 31 features these characteristics.

During the past two years the commercial airline operators and the travelling public alike have been forced to acknowledge the rapid increase in airport congestion. This problem is most marked in the North Eastern area of America at the present time but a similar situation will develop fairly soon at major airports in Europe. Even with the introduction of the airbus to scheduled services, the number of aircraft movements at conventional airports, within a given time period, will reach a maximum safe level. The restrictions are imposed partly by the large number of aircraft operations on each runway, and partly by Air Traffic Control safety limits.

The title proposed to me for this paper is not very suitable, as it suggests that I should cover two subjects, one of which, Present Supersonic Travel, is nonexistent, and the other, Future Supersonic Travel, is ,so vast that I could not possibly explore it fully in the time available.

Therefore, to clarify tonight's discussion, I shall define present and future supersonic aircraft as follows:

1. (a) Those aircraft now under construction and due to go into commercial service in the early seventies. This is primarily Concorde (if we leave out Eastern Europe).

2. (b) Those aircraft that will enter commercial service in the late ‘seventies and be flying in the ‘eighties, although I will discuss briefly the last decade of this century.

The pure torsional vibration of uniform thin-walled beams of open section, which is governed by the differential equation

has been extensively analysed by Gere He derived the exact frequency equations for beams with a variety of end conditions. However, these equations are, in most cases, highly transcendental.

This note uses an energy approach to obtain approximate frequency equations for the fixed-fixed and the fixed-simply-supported beams. A fixed end is one which allows no twist and no warping and a simply-supported end allows no twist but permits warping to take place freely. The approximating functions used are those corresponding to the exact solution of the problem if the torsional resistance caused by the St Venant system of shear stresses is zero. These functions are similar to the characteristic functions of simple beams in flexure.

The review of the literature suggests that the planar motion of a rigid satellite in a gravity gradient field has been the subject of considerable investigation during the past ten years. In contrast the dynamic study of a satellite executing librational motion out of the orbital plane has received comparatively little attention. Such an investigation is important because as pointed out by Kane, for large amplitudes the transverse motion is strongly coupled with that in the plane.

The lack of information may be due to the complex nature of the problem. The non-linear, non-autonomous, coupled equations of motion involving a large number of parameters are not amenable to simple, concise analysis. Some simplification may be achieved by restricting the satellite motion to a circular orbit. For this case, as indicated by Auelmann, closed zero-velocity curves exist under certain conditions which limit the amplitude of motion.

Exact solutions for certain types of non-linear systems where the non-linearity is symmetrical, that is to say, gravitational effects have been ignored, and damping is absent, are given by Den Hartog and Mikina. The algebra involved in these solutions is somewhat cumbersome and inconvenient to apply. A numerical method is given by Stormer but the computation is tedious without the use of a digital computer. The method employed by Lourie and Tchekmarev is commendable by virtue of its simplicity.

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”.

About 13 years ago rumours began to emerge from the USA of a hitherto unknown and mysterious condition afflicting the F100 and other contemporary fighter aircraft. In fast rolls these aircraft were said to experience gyrations in yaw and in pitch which by all accounts had no right to exist, especially as aerodynamically these configurations could not be faulted. After a burst of theoretical and experimental activity the condition was explained and the terms inertia cross-coupling, roll-coupling, roll yaw coupling and other synonyms became common currency in the world of aeronautics. The mystery of these puzzling manoeuvres was essentially solved. Unfortunately the problem was not. Cross-coupling has since become a major item on the agenda of the designer of every highspeed fighting aircraft and more recently it has also made some incursions in the area of the large slender aircraft.