The many methods by which Pontryagin's Maximum Principle is applied in optimal control problems can be divided into two groups, termed direct and indirect. The indirect methods use the conditions required for mathematical optimality as the starting point and attempt to satisfy the boundary conditions. The direct methods on the other hand satisfy the equations of motion and boundary conditions and then attempt to improve the performance index. It has been reported that the direct methods, while normally converging from very bad initial assumptions, have the inherent disadvantage of very slow convergence in the neighbourhood of the optimal solution and, so, complicated second order methods have recently been devised.

If air racing history is reviewed, it will be seen that the peak was reached when British light aircraft manufacturing was supreme. In 1927 alone, there were no fewer than 81 records set. The resurgence of interest following the Second World War declined until 1963 when only three records were set. Since then, air racing has progressed in one form or another to recent times when the Trans-Atlantic air race produced many new records. Unfortunately, this type of air race does little for the sporting aircraft enthusiast, and since the last Schneider Trophy Race, 40 years ago, there has not been a major international air race where aircraft have been pitted against each other to determine which flew the fastest.

The principle of wall similarity expressed by a universal logarithmic inner law relationship is well established for turbulent flow in circular pipes. The validity of Preston's original hypothesis for the measurement of turbulent skin friction depends upon the existence of wall similarity. Although Preston's hypothesis appears to be correct in general it has been found that his calibration for the wall pitot tube was incorrect. Extensive observations by Head and Rechenberg showed some discrepancy. Later work by Patel on the measurement of skin friction in three circular pipes covering a much larger experimental range has led to a modified calibration.

Until a few years ago it was the practice to neglect lift interference on oscillatory model tests in high-speed subsonic wind tunnels, whatever the working section configuration. However, in 1960 Bratt and Wight discovered a large interference effect on the pitch damping derivative of an M-wing measured in the slotted working section of the 25 in x 20 in tunnel at the National Physical Laboratory. In 1964 Wight reviewed a number of oscillatory tests and showed that in many cases there were significant interference effects on both stiffness and damping derivatives when measured in slotted working sections.

In a recent paper Garner discusses, among other topics, the induced (inviscid) drag or lift dependent drag, on finite wings which have effective antisymmetric incidence distributions. One example concerns a finite wing whose incidence varies linearly in the spanwise direction as

This wing experiences an overall induced drag which is made up from two contributions.

In a recent publication, Professor L. Dixon applied to a structural optimisation problem elements of the Pontryagin theory of optimal processes; well known in control systems. The problem considered was that of the minimum deflection of a cantilever beam under its own weight with constraints on the geometry. Digital and hybrid solutions of the two point boundary value problem arising from the optimisation problem were presented. Significant differences in the digital and hybrid solutions by the hill-climbing method were found. The present authors have examined the numerical methods for solving the optimisation equations, have developed a computing method which does not have the inherent convergence problem of the methods of Dixon, have re-examined the governing equation, and have noted a correction to these equations.

Shock expansion theory was first used by Epstein to calculate the characteristics of aerofoils with sharp leading edges and attached shock waves. In this case the aerofoil characteristics were found by assuming that the flow downstream of the leading edge shock was the same as in a Prandtl-Meyer expansion with all reflected waves neglected. In 1955 Eggers and Savin considered the extension of the method to three-dimensional hypersonic flows, with particular reference to bodies of revolution at incidence. Eggers and Savin point out that the most important factor influencing the method is the accuracy of the basic conical solution at the apex, since inaccuracies at the apex are reflected strongly in the pressures downstream. For this reason most applications of the method have been restricted to inclined bodies of revolution with pointed noses, since solutions for yawed cones can be used to start the solutions. Recently it has been shown that thin-shock-layer theory as originally developed by Messiter can give accurate solutions for the shock shapes and pressure distributions on the lower surfaces of conical bodies with a wide variety of cross-section shapes and for a wide range of hypersonic flight conditions.

The motion of liquid in the containers of a vehicle may have severe influence upon the stability of the vehicle. For this reason many authors have investigated the behaviour of liquid with a free surface due to various modes of excitation. In the earlier development of small vehicles, the frequencies of the elastic structures were relatively high compared to the propellant frequencies and the effect of their interaction could be neglected. With the increase of modern space vehicles this interaction of the propellant with the elastic structure is becoming a pronounced influence upon the design of the vehicle and its control system. This has some influence upon the stability and response behaviour of a large space vehicle, since the close grouping of propellant sloshing and structural frequencies around the control frequency of the vehicle creates continuous interaction during flight.

I was delighted and honoured to have been invited to give this lecture on the technical aspects of the Schneider Trophy and the world speed record attempts. Great Britain and Italy were the main contenders in the final and most exciting phase of the contest. As the Macchi aircraft were the most successful defenders of the Italian colours and, being myself the successor to Dr. Mario Castoldi, designer of the famous Macchi racers for the Schneider Trophy, I was very pleased to accept the kind invitation of the Society to give this lecture, especially in consideration of the fact that, as far as Macchi contribution is concerned, it was possible for me to collect first hand information directly from the people who actively collaborated with the racing effort.

The analogy between the formation of large amplitude waves (hydraulic jumps) on the surface of shallow flowing water, and shock waves in supersonic air flow is well-known. In addition to the correspondence between the wave patterns the variation in water depth can be related to the pressure distribution.

This “hydraulic analogy” is usually demonstrated in the laboratory in a tank which produces a shallow flow of water over a horizontal surface, on which the appropriately shaped body is mounted. The resulting stationary wave patterns may then be examined. Fig. 1 shows a typical bow-wave on a double-wedge.

In 1957 the Air Registration Board initiated a series of Technical Notes to provide a permanent record of technical work, generally in the form of specific investigations or research, performed by members of ARB staff. Although used to convey the results of such work to persons and organisations outside ARB, as well as for dissemination of the information within ARB, the ARB Technical Note series has never been publicised, and circulation has consequently been small and only to selected persons and organisations.

Wind tunnels are far older than powered flight. Including the aeroplane of the Wright Brothers, the introduction of new types of aircraft has almost invariably been preceded by extensive model investigation in wind tunnels. These investigations can be classified into two broad areas. One is development testing, in which models are tested and modified with the purpose of producing a specific aircraft configuration. The other covers the research and general experimentation which is necessary for the determination of the new rules governing entry into a new régime of flight. Thus, wind tunnels may conveniently be referred to either as “development” or as “research” wind tunnels, according to the type of work which is done in them.

Following the publication of my paper “Pilcher and the Multiplane” in the May issue of the Aeronautical Journal, I have had cause to reperuse the various accounts dealing with the operation of the “gust damping” device used by Chanute on his quadruplane and probably adopted by Pilcher for the multiplane.

Referring back to the original patents, which I had read thoroughly during the preparation of the paper, I realised that I had omitted to mention Chanute’s proposal of the deliberate operation of this system as a positive means of control.

For satellites that have part or all of their orbits extending into the earth's effective atmosphere, i.e. less than 500 miles, it is necessary to consider the contribution of the aerodynamic force in attitude dynamic studies. The importance of the aerodynamic torque is revealed by the fact that it is comparable to earth radiation at 500 miles, direct solar radiation at 400 miles, and depending on satellite geometry, can be as large as gravity gradient torque at 200-300 miles. Hence, in addition to solar and earth radiation torques, this paper includes the effect of the rarefied atmosphere on the response of gravity gradient satellites, thus covering the entire altitude range.