Practical problems often arise in which the aerodynamic loadings on wings and fins, due to nearby free vortices, are required. For example, aerodynamic loads on helicopter blades are affected by the tip vortices which are continuously being shed and which lie beneath the rotor plane. And vortices shed from the nose of an aircraft fuselage can induce significant side loads on a fin.

The estimation of the aerodynamic load distribution on a moving wing in the neighbourhood of a free vortex (whose axis is primarily in the free stream direction) is an interesting problem which, as far as the author is aware, has not been discussed previously in the literature. Standard techniques for conventional linearised wing theory cannot be applied directly to this problem because the trailing vorticity shed from the wing trailing edge is affected by the flow field of the free vortex and so the mathematical application of the Kutta trailing edge condition is more complex.

In 1970, at John F. Kennedy International Airport, New York, the value of international air cargo in and out is estimated at 5·9 thousand million dollars. That is about $16M on the average day. As in recent years, this will make JFK the number one customs port (sea or air) in the USA in terms of value of international cargo handled.

In 1969 at JFK some 409 000 short tons of international air cargo moved in and out, an average of 1263 tons or 2·5 million pounds per day. Using very rough conversion factors, this would fit into something like 500 containers 8 ft. by 8 ft. by 10 ft. This, of course, it not a real life illustration. Cargo comes in an infinite variety of shapes, sizes and weights—from massive machinery to fragile ladies’ garments on racks, from perishables to valuables.

Theoretical studies of the response of supersonic transport aircraft (SST) taxying and taking-off on uneven runways showed several years ago that the vertical acceleration in the cockpit of an SST of typical configuration would be greater than that in a subsonic transport on the same runway. The vibration would occur mainly at the frequency of bending of the fuselage, which might be 2 Hz, and would be forced by long, shallow undulations of the runway. These might have wavelengths of 50 ft to 300 ft (15 m to 90 m) and amplitudes of 1½ in to 4 in (0·04 m to 0·10 m) peak-to-peak, and are so unlike the usual concept of a rough surface that a different term, unevenness, is used to describe them.

Operational research is an attitude of mind and a collection of techniques. Although the people who make up the engineering strength of a guided weapons firm find that attitude of mind congenial and commonly approach their problems predisposed to use the techniques, it is uncommon to encounter an OR group in any great strength.

This is perhaps because the grouping of people by techniques in such firms is more natural when those techniques bear a direct relation to the firm's products. Despite the fact that a substantial body of practitioners is not to be found in close association, practices which are recognisable as OR are to be found throughout the course of a project.

The free vibration of an elastic system represented by a finite number of degrees of freedom leads to the problem of determining the eigenvectors and eigenvalues of the equation

where K and M are symmetric matrices of order n, and x is an n-dimensional vector of generalised co-ordinates. Under certain circumstances as, for example, when the matrices are of large order and only a few eigenvalues and eigenvectors are required, it is preferable to use an iterative procedure for solving eqn. (1) or an equation equivalent to it. However, when the system has one or more rigid-body degrees of freedom the stiffness matrix K is singular. This precludes an iterative solution.

The modern jet transport has established an excellent safety record of which the industry can justly be proud, but with the airlines soon to be flying something of the order of a million hours per month, the potential exposure to accident in the years ahead is considerable.

The first 50M hours of jet flight took 12 years to achieve and—excluding the wanton destruction of aircraft in the Middle East—involved the loss of 132 aircraft and the deaths of 3800 passengers, or an average of aircraft and 76 passengers per million hours. Isolation of the past three years of this record to detect the later trend reveals an improvement to an average of 2 aircraft and 51 passengers per million hours. Given no further improvement this would soon become the average monthly rate of loss, but because of the uncertainty as to the passenger load factor in any particular accident, consideration must now be given to the realistic possibility of losing at least 20 aircraft and perhaps 1000 or more passengers in any one year. Given the validity of this concept, then over the next five years whatever dollar figure is chosen to represent the financial problem involved, the first digit is likely to be followed by nine noughts!

I would like to make this talk as non-provocative as possible. I want to talk about VTOL: I do not want to compare VTOL with STOL, although it is necessary to make a comparison with ordinary aeroplanes because one must have an economic datum.

Hawker Siddeley's interest in VTOL, or more properly V/STOL, arises at least partly from experience on the Harrier. Unlike the Harrier, future civil aircraft will of course need to have multiple engines of very low jet velocity, for low noise and safety. These VTOL elements have however already been demonstrated in flight separately (on such aircraft as the SC-1, Dornier Do31 and Ryan XV-5) but not yet together. From what we know about the trends of engine technology, and from a fairly intensive project and research programme on civil V/STOL over the past few years, we have arrived at V/STOL designs with operating costs and noise characteristics rather better than those suggested by BAC. However, I think we would agree with a very great deal of what Mr. Quick has said about STOL. In our view, VTOL and STOL are by no means mutually exclusive … there is likely to be a future market for all kinds of aeroplanes whether they are STOL, V/STOL, RTOL, CTOL, or whatever.

The majority of current prediction procedures for turbulent flows employ models of turbulent momentum transfer which calculate an effective viscosity for μeff such that for a boundary-layer flow the shear stress, τ, is given by:

A number of recent experimental investigations (ref. 1-3 for example) have found, however, that in strongly asymmetric turbulent flows, τ is finite where the mean velocity gradient is zero—and vice versa. These phenomena, which are evidently not describable in terms of an effective viscosity hypothesis, point the need for a more complete description of turbulent motion.

The concept of stability under constraint had been developed by Neumark and applied with considerable success to predict the speed instabilities in the flight of aircraft below minimum drag speed. This concept involves the removal (or partial removal) of one or more degrees of freedom of an aircraft by the deliberate application of some control to keep a chosen element of disturbance at a constant value. A partial constraint could thus be introduced in practice by a pilot trying to keep the wings level with the horizon by the use of aileron control, or keeping attitude constant with the use of elevator. Pinsker has recently used bank angle constraint stability of an aircraft as a means of defining a minimum acceptable value of nv.

This present note considers some aspects of longitudinal stability under constraint as applicable to the flight of a helicopter in the forward and the hover modes.

In many applications of boundary-layer control by tangential blowing the surface downstream of the blowing slot is likely to be strongly curved. For example, this is the case when blowing around a bluff trailing edge is used to control the circulation around an aerofoil as described in ref. 1. The flow involved in such cases is that of a curved wall jet in an adverse pressure gradient. A knowledge of the radial and tangential pressure distributions in the curved wall jet is required if development of the flow and separation are to be predicted.

The problem of vibrations of a circular ring on an elastic foundation finds application in the study of vibrations of gears mounted on elastic shafts and launching vehicles having a ring-stiffened shell structure.

The inplane flexural vibrations of a circular ring were investigated by many authors in connection with the study of vibrations of gears and frames of electrical machines. The transverse vibrations of a thin ring of circular cross-section were first investigated in 1890 by Michell. There appears to be less amount of work in the literature which deals with the effects of rotatory inertia and shearing deformation on the transverse vibrations of rings. In the present investigation, flexural vibrations of a circular ring on an elastic foundation involving both displacements at right angles to the plane of the ring and twist are studied. The foundation is considered to provide restraints against the transverse and torsional motions of the cross-section of the ring linearly.