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The use of Dimensional Analysis in aerodynamics: an historical note

Published online by Cambridge University Press:  04 July 2016

J. C. Gibbings*
Affiliation:
Fluid Mechanics Division, Department of Mechanical Engineering , University of Liverpool

Extract

A private enquiry about the initial application of Dimensional Analysis to experimental measurements in aerodynamics has been made of the writer. The consequent literature search has revealed what is now to be described. If due credit is to be given correctly the matter needs checking particularly by those who had direct contact with the early aerodynamicists throughout the world: initiation of that check is the reason for this paper. Dimensional Analysis originally came from ideas of similarity which were considered by such masters as Kepler, Newton and Galileo. The idea of equality of dimensions in an equation was used by Fourier. Dimensional Analysis was, after Galileo, used by biologists in the last century but in the general area of physics the initial impetus came from Rayleigh. Rayleigh first advocated the value of Dimensional Analysis in 1885 and though he usually referred to it as a method of similitude he also, despite what has often been written to the contrary, used the description of ‘method of dimensions’.

Type
The Real Cost of Air Transport
Copyright
Copyright © Royal Aeronautical Society 1982 

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References

1. Szucs, E. Similitude and modelling. Elsevier. Amsterdam 1980. 3233.Google Scholar
2. Newton, I. Philosophiae naturalis principia mathematica. Lib ii, Prop 32. 1686 (Trans V Calif Press, 1962).Google Scholar
3. Fourier, J. B. J. Theorie analytique de lachaleur, 2, Sec 7. Ch2 Sec 9. 135140. Firmin Didot. Paris 1822.Google Scholar
4. Thompson, , D’arcy, W. The Principle of Similitude. Nature. 95, 202. 22nd April 1915.Google Scholar
5. Rayleigh, Lord. Review: Professor Tait’s Properties of matter. Nature. 32, 314. 6th August 1885.Google Scholar
6. Rayleigh, Lord. On the question of the stability of the flow of fluids. Phil Mag. 34, 5970. 1892 (Also: On the viscosity of argon as affected by temperature. Proc Roy Soc. 66, 68-74. 1900).Google Scholar
7. Stokes, G. G. On the effect of the internal friction of fluids on the motion of pendulums. Trans Camb Phil Soc. 9, Pt 2. No. 10, 8106 (1856). (Read 9th December 1850).Google Scholar
8. Reynolds, O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels. Phil Trans Roy Soc. 174, 935. 15th March 1883. (See also Br Assoc Report 1889).Google Scholar
9. Technical Report, Advisory Committee for Aeronautics 1910-1911. 113.Google Scholar
10. Rayleigh, Lord. Fluid friction on even surfaces. Phil Mag. 8 (6th Ser). July-December 1904. 66.Google Scholar
11. Annual report of the Aeronautical Society of Great Britain. 1, 7576. London 1871.Google Scholar
12. McTarland, M. W. (Ed). The papers of Wilbur and Orville Wright, McGraw-Hill, New York, 1953.Google Scholar
13. Advisory Committee for Aeronautics. Report 1910-1911, 122123.Google Scholar
14. Bacon, R. H. Report of Advisory Committee for Aeronautics 1909-10. R&MNo. 1. 12th May 1909, 132.Google Scholar
15. Stanton, T. E. Report on recent researches on the forces on plane surfaces in a current of air. ACA Report 1909-10. R&M No. 4. 22nd May 1909.Google Scholar
16. Rayleigh, Lord. Note as to the application of dynamical similarity. Report of the Advisory Committee for Aeronautics. 1909-10. R&M No. 15. 23rd June 1909. Pt. 2, 38.Google Scholar
17. Report of the Advisory Committee for Aeronautics 1910-11. 109, 113, 115.Google Scholar
18. Giacomelli, R. and Pistolesi, E. Historical sketch. Aero dynamic theory. (Ed. Durand, W. F.). 1, 363.Google Scholar
19. Bairstow, L. and Booth, H. The principle of dynamical similarity in reference to the results of experiments on the resistance of square plates normal to a current of air. ACA Report 1910-11. R&M No. 38,21. March 1911.Google Scholar
20. Rayleigh, Lord. The principle of dynamic similarity in reference to the results of experiments on the resistance of square plates normal to a current of air. ACA Report 1910-11. R&M No. 39. 26. March 1911.Google Scholar
21. Melville-Jones, B. The resistance of wires and ropes in a current of air. ACA Report 1910-11. R&M No. 40. Pt. 1, 40. March 1911.Google Scholar
22. Karman, Von, Th. Ueber die Turbulenzreibung vershiedener Flussigk’eiton. Physikalisch Zeitschrift. 12, No. 8. 283284. 15th April 1911.Google Scholar
23. Rayleigh, Lord. Sur la resistance des spheres dan l’air en mouvement. Comptes Rendus 156, 109. 13th January 1913.Google Scholar