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.

This paper is the first of a series of three which are concerned with the subject of “ hysteretic damping.” This type of damping, in a simple system with one degree of freedom, is like the familiar “ viscous damping ” in that it implies a resisting force which is in phase with velocity; but it is unlike viscous damping in that the magnitude of the force is not proportional to the velocity but to the displacement. When a system has n degrees of freedom, hysteretic damping implies that damping forces exist which are proportional to relative displacement but which are in phase with relative velocity.

From a physical standpoint, hysteretic damping may give a better representation of the facts when the damping arises from the internal friction of solid materials. On the side of theory, it raises considerations which it is the purpose of these three papers to elucidate. It may be said, at the outset, that the notion of hysteretic damping raises no great mathematical difficulty; on the contrary, a main reason for presenting the theory is that it appears to allow of a much simpler discussion (than does viscous damping) of the nature of steady damped oscillation of systems having n degrees of freedom.

In the first paper, the purpose is discussed of mathematical theories of damping in vibration theory. It is concluded that the theory of “ hysteretic damping ” is a useful one since it provides an alternative to the fiction of “ viscous ” damping while retaining the mathematical linearity of equations of motion. The word “ hysteretic” is proposed for use in this sense instead of the previously used adjective, namely “ structural.” “ Complex damping ” is related to hysteretic damping in a way which is explained.

The theory is given for forced oscillations of a system with one degree of freedom. It is shown that free vibration cannot be treated satisfactorily unless the definition of hysteretic damping is widened in some way to cover non-harmonic motion.

The aerodynamic characteristics of airframes are expressed as aerodynamic transfer functions, giving the relationships between input and output for each of the three separate planes of motion, roll, pitch, and yaw. By assuming no cross-coupling between planes and linear aerodynamics, and by making certain other assumptions, which apply particularly to conventional airframes with fixed wings and rear controls, relatively simple approximate algebraic transfer functions giving the relationships between the control surface deflection (the input) and any airframe motion (the output), are obtained.

The open loop aerodynamic transfer functions thus obtained are used as part of the auto-pilot block diagram, in which the performance of other components, such as actuators, instruments and electrical networks, are also expressed in transfer function form. The aerodynamic transfer functions are useful in auto-pilot evolution and synthesis in that they aid selection of the airframe motions to be measured, modified, and fed back to close the auto-pilot loop.

For mathematical assessment of closed loop performance and stability, open loop transient and frequency responses are used, and curves of airframe responses are plotted in linear, logarithmic and polar form by standard methods from the aerodynamic transfer functions. Some methods of using these curves, which follow the general lines adopted in servo-mechanism and electronic amplifier design, are explained briefly.

Analogue computers are frequently used when the computations to be made are so complicated as to need the use of a computing machine. The aerodynamic transfer functions then form one block of the simulator set-up, and on larger computers the more exact form, including any non-linearities and cross-coupling effects, can be used.

It is always difficult and sometimes dangerous to estimate future trends and events. Nevertheless, it is a most satisfactory outlet for one's imagination and it is, to some extent, necessary unless we are to abandon all attempts at shaping our own future.

Before trying to forecast the future of the helicopter, I feel that I must define what I mean by a helicopter. Resort to the English Dictionary does not help greatly; as is so often the case, it has been left behind by progress.

A helicopter is described as “a flying machine that should rise vertically by airscrews revolving horizontally.” Derivation from the Greek, helix—a spiral, and pteron—a wing. This definition indicates that every aeroplane having a thrust loading of less than one is a helicopter, unless it is propelled by rockets, ramjets or pulse jets!

The dictionary definition of an aeroplane is “ a flying machine heavier than air using planes.”

A new method for evaluating determinants or matrices is given; it is rather tedious to describe and awkward to prove, but is very easy to use. The chief advantages this method is believed to possess are:

1. (i) It involves as few arithmetical manipulations as does the most rapid method of pivotal condensation currently used.

2. (ii) It is easier than any other known method to learn and to remember.

3. (iii) It can be adapted to routine computation, in such a way as to minimise the likelihood of error.

4. (iv) A digital computor can readily be programmed to use it.

The laws of reflection of pressure waves at temperature discontinuities are well known. Of particular interest is the effect of temperature discontinuities on the pressure conditions in the exhaust pipes and cylinders of two-stroke cycle engines, both models and running engines. Model experiments are usually performed at low temperatures with the cylinder release temperature and exhaust pipe temperatures of the same order; under these conditions the reverse type of temperature phenomenon occurs to that in running engines with excess scavenge air. In the case of a model during the exhaust blowdown the gas from the cylinder reaches the exhaust pipe with a greater density than that of the gas initially in the exhaust pipe.

The problem of bending of thin elastic plates has interested mathematicians and engineers for many years. Various methods have been put forward for determining the approximate solutions among which the variational method of Ritz is most common. This procedure leads to a system of linear simultaneous equations, the solution of which is often quite tedious, although generally by taking a few rows and columns quite accurate results are obtained. The purpose of this note is to show that by using bar eigen-functions for plates which are either clamped, or when some edges are freely supported, certain simplifications can be made in the process and the difficulty of solving simultaneous equations can be avoided; and that the deflection surface of the plate can be derived directly in a series form.