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Mathematics and Aeronautics

Published online by Cambridge University Press:  04 July 2016

M. J. Lighthill
M. J. Lighthill*
Affiliation:
Royal Aircraft Establishment
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Abstract

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.

Type
The Forty-Eighth Wilbur Wright Memorial Lecture
Information
The Aeronautical Journal , Volume 64 , Issue 595 , July 1960 , pp. 375 - 394
Copyright
Copyright © Royal Aeronautical Society 1960

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References

1.Wilbur, Wright and Orville, Wright (1953). Papers, Vol. 1, pp. 5 and 15, McGraw-Hill, 1953.Google Scholar
2.Prandtl, L. (1904). Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandl. d. 111. Internal. Math. Kongr. (Heidelberg). Teubner, p. 484, 1904.Google Scholar
3.Kutta, W. M. (1902). Auftriebskrafte in stromenden Flüssigkeiten. Illustr. aeronaut. Mitteilungen, p. 133, 1902.Google Scholar
4.Blasius, H. (1910). Funktiontheoretische Methoden in der Hydrodynamik. Zeit. f. Math. u. Phys. 58, p. 90, 1910.Google Scholar
5.Joukowski, N. (1916). Aérodynamique. Gauthier Villars, 1916.Google Scholar
6.Chaplygin, S. A. (1909). Precise Reference Unknown, but see Landau, L. D. and Lifshitz, E. M.Fluid Mechanics, p. 174. Pergamon, 1959.Google Scholar
7.Lanchester, F.W. (1909). Aerodynamics. Constable, 1909.Google Scholar
8.Prandtl, L. (1918, 1919). Tragflügeltheorie. Nachr. d. K. Gesell. d. Wiss. zu Gött., Math.-Phys. Klasse, pp. 451–477, 1918, and 107-137, 1919.Google Scholar
9.Bryan, G. H. and Williams, W. E. (1904). The Longitudinal Stability of Aerial Gliders. Proceedings of the Royal Society 73, p. 100, 1904.Google Scholar
10.Bryan, G. H. (1911). Stability in Aviation. Macmillan, 1911.Google Scholar
11.Nyquist, H. (1932). Regeneration Theory. B.S.T.J. 11, p. 126, 1932.Google Scholar
12.Lighthill, M. J. (1954). Mathematical Methods in Compressible Flow Theory. Comm. Pure and Appl. Math. 1. p. 1, 1954.CrossRefGoogle Scholar
13.Hollingdale, S. H. (1959). The Application of Automatic Digital Computers to Aeronautics. Journal of the Royal Aeronautical Society, 63, p. 51, 1959.CrossRefGoogle Scholar
14.Kopal, Z. (1947, 1949). Tables of Supersonic Flow Around Cones, Tables or Supersonic Flow Around Yawing Cones and Tables of Supersonic Flow Around Cones of Large Yaw. Massachusetts Institute of Technology, 1947, 1947 and 1949.Google Scholar
15.Munk, M. M. (1924). The Aerodynamic Forces on Airship Hulls. Nat. Adv. Comm. Aero. (Washington) Rep. 184, 1924.Google Scholar
16.Von Kármán, TH. and Moore, N. B. (1932). Resistance of Slender Bodies Moving With Supersonic Velocities, With Special Reference to Projectiles. Transactions American Society Mechanical Engineers 54, p. 303, 1932.Google Scholar
17.Tsien, H. S. (1938). Supersonic Flow Over an Inclined Body of Revolution. Journal Aeronautical Sciences 5, p. 480, 1938.CrossRefGoogle Scholar
18.Jones, R. T. (1946). Properties of Low-Aspect-Ratio Pointed Wings at Speeds Below and Above the Speed of Sound. Nat. Adv. Comm. Aero. Rept. (Washington) 835, 1946.Google Scholar
19.Lighthill, M. J. (1945). Supersonic Flow Past Bodies of Revolution. A.R.C. R. & M. 2003, 1945.Google Scholar
20.Lighthill, M. J. (1948). Supersonic Flow Past Slender Pointed Bodies of Revolution at Yaw. Quarterly Journal Mechanics and Applied Mathematics 1, p. 76, 1948.Google Scholar
21.Ward, G. N. (1949). Supersonic Flow Past Slender Pointed Bodies. Quarterly Journal Mechanics and Applied Mathematics 2, p. 75, 1949.Google Scholar
22.Ward, G. N. (1955). Linearized Theory of Steady High speed Flow. Cambridge University Press, 1955.Google Scholar
23.Von Karman, TH. (1935). The Problems of Resistance in Compressible Fluids. Proc. 5th Volta Conference (Rome), p. 255, 1935.Google Scholar
24.Whitcomb, R. T. (1952). A Study of the Zero-lift Drag- rise Characteristics of Wing-body Combinations Near the Speed of Sound. Nat. Adv. Comm. Aero. (Washington), Research Memorandum No. L.52. H.08.Google Scholar
25.Whitham, G. B. (1952). The Flow Pattern of a Supersonic Projectile. Comm. Pure and Appl. Math. 5, p. 301, 1952.Google Scholar
26.Allen, H. J. and Perkins, E. W. (1951). A Study of Effects of Viscosity on Flow Over Slender Inclined Bodies of Revolution. Nat. Adv. Comm. Aero. (Washington) Rep. 1048, 1951.Google Scholar
27.Heaslet, M. A. and Lomax, H. (1954). Supersonic and Transonic Small Perturbation Theory. Section D of General Theory of High Speed Aerodynamics. (Ed. W. R. Sears.) Princeton Univ. Press, 1954.Google Scholar
28.Lighthill, M. J. (1949). The Drag Integral in the Linearized Theory of Compressible Flow. Quarterly Journal Mathematics (Oxford), 20, p. 121, 1949.CrossRefGoogle Scholar
29.Sears, W. R. (1947). On Projectiles of Minimum Wave Drag. Quarterly Applied Mathematics 4, p. 361, 1947. 24. Google Scholar
30.Haack, W. (1941). Geschossformen Kleinsten Wellen- widerstandes. Lilienthal-Gesellschaft Bericht, 139, p. 14, 1941.Google Scholar
31.Lighthiix, M. J. (1956). The Wave Drag at Zero Lift of Slender Delta Wings and Similar Configurations. Journal Fluid Mechanics 1, p. 337, 1956.Google Scholar
32.Keune, F. (1956). Forschungsberichte des Wirtschafts— und Verkehrs—Ministeriums der Nordrhein-Westfalen, No. 316, 1956.Google Scholar
33.Keune, F. and Oswatitsch, K., (1956). On the Influence of the Geometry of Slender Bodies of Revolution and Delta Wings on Their Drag and Pressure Distribution at Transonic Speeds. Roy. Inst. Tech. (Stockholm) K.T.H. Aero. T.N. No. 42, 1956.Google Scholar
34.Lighthill, M. J. (1953). Oscillating Airfoils at High Mach Number. Journal Aeronautical Sciences 20, p. 402, 1953.Google Scholar
35.Hayes, W. D. and Probstein, R. F. (1959). Hypersonic Flow Theory. New York: Academic Press, 1959.Google Scholar
36.Maskell, E. C. and Weber, J. (1959). On the Aero dynamic Design of Slender Wings. Journal of the Royal Aeronautical Society 63, p. 709, 1959.Google Scholar
37.Ferrari, C. (1957). Interaction Problems, Section C of Aerodynamic Components of Aircraft at High Speeds. (Ed. Donovan, A. F. and Lawrence, H. R..) Princeton Univ. Press, 1957.Google Scholar
38. Unpublished Work by Broadbent, E. G. and Zbrozek, J. K..Google Scholar
39.Lighthill, M. J. (1960). Note on the Swimming of Slender Fish. To be Published in Journal Fluid Mechanics.Google Scholar
40.Lighthill, M. J. (1948). Supersonic Flow Past Slender Pointed Bodies of Revolution at Yaw. Quarterly Journal Mechanics and Applied Mathematics 1, p. 76, 1948.Google Scholar
41.Broderick, J. B. (1949). Supersonic Flow Around Pointed Bodies of Revolution. Quarterly Journal Mechanics and Applied Mathematics 2, p. 98, 1949.CrossRefGoogle Scholar
42.Lighthill, M. J. (1954). Higher Approximations. Section E of General Theory of High Speed Aerodynamics. (Ed. Sears, W. R..) Princeton Univ. Press, 1954.Google Scholar
43.Brown, C. E. (1957). Aerodynamics of Bodies at High Speeds. Section B of Aerodynamic Components of Air craft at High Speeds. (Ed. Donovan, A. F. and Lawrence, H. R..) Princeton Univ. Press, 1957.Google Scholar
44.Jones, R. T. and Cohen, D. (1957). Aerodynamics of Wings at High Speeds. Section A of Aerodynamic Components of Aircraft at High Speeds. (Ed. Donovan, A. F. and Lawrence, H. R..) Princeton Univ. Press, 1957.Google Scholar
45.Frick, C. W. (1957). The Experimental Aerodynamics of Wings at Transonic and Supersonic Speeds. Section G of Aerodynamic Components of Aircraft at High Speeds. (Ed. Donovan, A. F. and Lawrence, H. R..) Princeton Univ. Press, 1957.Google Scholar
46.Lighthill, M. J. (1948). Supersonic Flow Past Slender Bodies of Revolution, the Slope of Whose Meridian Section is Discontinuous. Quarterly Journal Mechanics and Applied Mathematics 1, p. 90, 1948.Google Scholar
47.Butler, D. S. (1960). The Numerical Solution of Hyper bolic Systems of Partial Differential Equations in Three Independent Variables. Proceedings Royal Society A, 255, p. 232, 1960.Google Scholar
48.Walkden, F. (1959). On the Numerical Calculation of Three-dimensional Supersonic Flows. Ph.D.Thesis, Manchester University, 1959.Google Scholar
49.Mangler, K. W. and Smith, J. H. B. (1959). A Theory of the Flow Past a Slender Delta Wing With Leading Edge Separation. Proceedings of the Royal Society A. 251, p. 200, 1959.Google Scholar
50.Roy, M. (1952). Caractères de l'écoulement autour d'une aile en flèche accentuée. C. R. Acad. Sci. (Paris), 234, p. 2501, 1952.Google Scholar
51.Legendre, R. (1952-3). Écoulement au voisinage de la pointe avant d'une aile à forte flèche aux incidences moyennes. Rech. Aero. 30, p. 3; 31, p. 3; 35, p. 3.Google Scholar
52.Morgan, M. B. (1960). Supersonic Aircraft—Promise and Problems. Journal of the Royal Aeronautical Society, p. 315, June 1960.Google Scholar