The 48th Wilbur Wright Memorial Lecture, “Mathematics and Aeronautics” was given by Mr. M. J. Lighthill, F.R.S., before a large and distinguished audience at the Institution of Mechanical Engineers, 1 Birdcage Walk, on 19th May 1960. Dr. E. S. Moult, C.B.E., B.Sc, F.R.Ae.S., M.I.Mech.E., President of the Society, presided.

As has become the custom, before the lecture was delivered the President presented the awards made by the Council for 1960 for outstanding contributions to aeronautics. In the unavoidable absence of the Secretary he was assisted by Miss E. C. Pike, M.A., A.F.R.Ae.S., Secretary of the Medals and Awards Committee and Editor of The Aeronautical Quarterly. The list of the awards presented on this occasion was published in the June 1960 Journal—(p. XXXII).

The President, introducing the lecturer, reminded the audience that the Wilbur Wright Lecture commemorated the first manned, powered controlled flight by Wilbur Wright at Kitty Hawk, North Carolina on 17th December 1903. The first Wilbur Wright Memorial Lecture was held in 1913 and they had been held each year ever since, through two World Wars; in itself a wonderful record. The custom had been, and would continue to be, to have alternately a lecturer from the United Kingdom and a lecturer from the United States; last year the lecture had been by Mr. McCarthy of Chance Vought and next year again it would be by an American.

The Wilbur Wright Lectures had been a most distinguished series by distinguished lecturers, and he was sure that the lecture that night would be in keeping. His pleasant duty was to introduce Professor Lighthill—or as they had to call him Mr. Lighthill now that he was Director of the Royal Aircraft Establishment, which was an even greater distinction. Mr. Lighthill was the youngest Director that the R.A.E. had ever had—that alone was a tribute to Mr. Lighthill's ability and his high standing in the profession. Before joining the Royal Aircraft Establishment Mr. Lighthill was Professor of Applied Mathematics at Manchester University, and for a time, after leaving Cambridge, had worked at the National Physical Laboratory where he applied the mathematics of Cambridge to the problems of aerodynamics. His lecture was on “Mathematics and Aeronautics” he would ask Mr. Lighthill to deliver the 48th Wilbur Wright Memorial Lecture.

The Revival of interest in flight by man's own muscle power brings back to me some early attempts to solve this problem some 30 years ago.

Needless to say I was—and still am—sold on this idea ever since reading Lilienthal's famous book as a youngster in school. Then came the Wright Brothers and the early years of flying and the years of the First Great War at the end of which I found myself as an Aerodynamicist, designing wing sections and calculating induced drag according to Prandtl's newly discovered wing theory.

The end of the war found us meditating about gliding and the possibility of soaring flight. And so came the Rhoen, and the “Sturm und Drang” of the years on the Wasserkuppe.

The subject matter of this paper is primarily an account of operational experience over a comparatively short period resulting from helicopter activities at the Westland London Heliport. At the outset it is appropriate to recall publication by the Helicopter Association of Great Britain, in January, 1958, of a widely circulated report entitled “Examination of the Case for a London Heliport”. There in was expressed the opinion that there existed an immediate need for an operating base in the inner metropolitan area for use by single-engined helicopters. Further, that it was mistaken policy for the then Ministry of Transport and Civil Aviation to relate the need for a London heliport to the future advent of multi-engined helicopters. In the meantime the initiative had been taken by Westland Aircraft as a private venture to provide a suitable site, and to accept financial responsibility for all procedural and constructional work associated with its development and operation.

The paper mainly discusses recent R.A.E. and N.P.L. research on the aerodynamics of Direct jet lift (turbo-jet and turbo-fan), Propeller lift (tilt-wing and deflected slipstream), Jet flaps, and Boundary layer control (blowing and suction). Some of the work at Firms and Universities is also mentioned where the information has been made available for general circulation. Attention is drawn to the present state of knowledge in relation to V.T.O.L. and S.T.O.L. aircraft applications and to some major aerodynamic problems which need further study.

As is well known, the analysis of shock waves is complicated when the gas becomes dissociated on passage through the wave. As well as showing a dependence on the Mach number of the incident flow and non-dimensional quantities characteristic of the nature of the gas, as does the analysis when applied to a perfect gas, it then also shows a dependence on the thermodynamic state of the upstream air, as described for instance by its temperature and pressure. A growing number of calculations is becoming available, especially for air in complete thermal and chemical equilibrium, but the interpolation to give results appropriate to the three independent variables (of upstream state and incident velocity) needed in any particular application can often be rather troublesome, and one has still less faith in extrapolation.