Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T21:31:42.563Z Has data issue: false hasContentIssue false
  • English
  • Français

The Theory of Aerofoils in Unsteady Motion

Published online by Cambridge University Press:  07 June 2016

J. R. M. Radok
J. R. M. Radok*
Affiliation:
Department of Supply and Development, Aeronautical Research Laboratories, Melbourne
Get access

Summary

The theory of aerofoils in unsteady flow, which has made substantial progress in the last decade due largely to the ground work of Küssner and his co-workers, is presented here in a form suitable for application in aeroelastic problems, particularly those concerned with the dynamic loads on aircraft arising from gusts.

Exact expressions are given for the aerodynamic lift and moment for an oscillating aerofoil as well as for the case of arbitrary motion through disturbed air. The expressions for the latter case involve two special functions, generally referred to as Wagner and Küssner functions. Exact values of these functions are tabulated together with useful approximations. The problem of a wing-tail combination is discussed and a method of solution indicated. The bibliography at the end of the paper lists the most important publications in this field.

Type
Research Article
Information
Aeronautical Quarterly , Volume 3 , Issue 4 , February 1952 , pp. 297 - 320
Copyright
Copyright © Royal Aeronautical Society. 1952

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References and Bibliography

1. Lycn, H. M. (1937). A Review of Theoretical Investigations of the Aerodynamical Forces on a Wing in Non-uniform Motion. R. & M. 1786, 1937.Google Scholar
2. Küssner, H. G. (1936). Zusammenfassender Bericht über den instationären Auftrieb von Flügeln. Luftfahrtforschung, Vol. 13, 1936, pp. 410–424.Google Scholar
3. Cicala, P. (1941). Present State of Research on the Non-steady Motion of a Lifting Wing. L'Aerotechnica, Vol. 19, pp. 557–591, 670-685, 759-773, Sept.-Dec. 1941 (R.T.P. 1867).Google Scholar
4. Jones, W. Prichard (1942). Summary of Formulae and Notations Used in Two-dimensional Derivative Theory. R. & M. 1958, 1942.Google Scholar
5. Küssner, H. G. and Schwarz, L. (1940). Der schwingende Flügel mit aerodynamisch ausgeglichenem Ruder. Luftfahrtforschung, Vol. 17, 1940, pp. 337–354.Google Scholar
6. Küssner, H. G. (1940). Das zwei-dimensionale Problem der beliebig bewegten Tragfläche unter Berüksichtigung von Partial-bewegungen der Flüssigkeit. Luftfahrtforschung, Vol. 17. 1940. pp. 355–361.Google Scholar
7. Theodorsen, T. (1934). General Theory of Aerodynamic Instability and the Mechanism of Flutter. N.A.C.A. Report 496, 1934.Google Scholar
8. Küssner, H. G. (1935). Augenblicklicher Entwicklungs-stand der Frage des Flügelflatterns. Luftfahrtforschung, Vol. 12, 1935.Google Scholar
9. Küssner, H. G. (1929). Schwingungen von Flugzegflügeln. Luftfahrtforschung, Vol. 6, 1929.Google Scholar
10. Küssner, H. G. (1936). Untersuchung der Bewegung einer Platte beim Eintritt in eine Strahlgrenze. Luftfahrtforschung, Vol. 13, 1936, pp. 425–429.Google Scholar
11. Jaeckel, Karl (1939). Uber die Bestimmung der Zirkulations-verteilung für den zwei-dimensionalen Tragflügel bei beliebigen periodischen Bewegungen. Luftfahrtforschung, Vol. 16, 1939, pp. 135–138.Google Scholar
12. Jaeckel, Karl (1939). Eine Formel für die von einem dünnen Tragflügel-profil induzierte Geschwindigkeit in Punkten die auf der verlängerten Sehne liegen. Luftfahrtforschung, Vol. 16, 1939, p. 53.Google Scholar
13. Garrick, I. E. (1938). On Some Reciprocal Relations in the Theory of Non-stationary Flows. N.A.C.A. Report 629, 1938.Google Scholar
14. Garrick, I. E. (1939). On Some Fourier Transforms in the Theory of Non-stationary Flows. Proceedings, 5th International Congress of Applied Mechanics, Cambridge, Mass., 1939.Google Scholar
15. Wagner, H. (1925). Uber die Entstehung des dynamischen Auftriebes von Tragflügeln. Z. Angew. Math. Mech. Bd. 5, 1935, p, 17.CrossRefGoogle Scholar
16. Schwarz, L. (1940). Berechnung der Functionen U 1(s) and U 2(s) für gröszere Werte von s. Luftfahrtforschung , Vol. 17, 1940, pp. 362–369.Google Scholar
17. von Kárman, Th. and Sears, W. R. (1938). Airfoil Theory for Non-uniform Motion. Journal of the Aeronautical Sciences, Vol. 5, August 1938, pp. 379–390.Google Scholar
18. Jones, R. T. (1939). The Unsteady Lift of a Finite Wing. N.A.C.A. T.N. 682, 1939.Google Scholar
19. Jones, R. T. (1940). The Unsteady Lift of a Wing of Finite Aspect Ratio. N.A.C.A. Report 681, 1940.Google Scholar
20. Jones, W. Prichard (1945). Aerodynamic Forces on Wings in Non-uniform Motion. R. & M. 2117, 1945.Google Scholar
21. Jenkins, E. S. and Pancu, C. D. P. (1948). Dynamic Loads on Airplane Structures. Presented at S.A.E. National Aeronautic and Air Transport Meeting, New York City, April 1948.Google Scholar
22. Glauert, H. (1929). The Accelerated Motion of a Cylindrical Body through a Fluid. R. & M. 1215, 1929.Google Scholar
23. Greidanus, J. H. (1947). The Loading of Aeroplane Structures by Symmetrical Gusts. Reports and Transactions of the Nat. Aeronaut. Res. Inst., Amsterdam, Vol. XIV, 1947.Google Scholar
24. Greidanus, J. H. and van de Vooren, IR. A. I. (1948). Gust Load Coefficients for Wing and Tail Surfaces of an Aeroplane. Nat. Luchtvaartlab., Amsterdam. Report F.28.Google Scholar
25. van de Vooren, A. I. (1948). Remarks on Formulae and Numerical Methods Used in Report F.28. Nat. Luchtvaartlab., Amsterdam. Report F.29.Google Scholar
26. van de Vooren, A. I. (1948). Loads on Wing and Tail Surfaces of an Aeroplane Due to a Sinusoidal Gust Wave. Nat. Luchtvaartlab., Amsterdam. Report F.33.Google Scholar
27. Greidanus, J. H. and van de Vooren, IR. A. I. (1949). Proposal for an Airworthiness Requirement Referring to Symmetrical Gust Loads. Nat. Luchtvaartlab., Amsterdam. Report F.45.Google Scholar
28. Curtis, A. R. (1946). On a Method of Calculating the Response of an Aeroplane to a Vertical Gust of Known Form. A.R.C. 9700, S. & C. 2021, June 1946.Google Scholar
29. Curtis, A. R. (1947). The Acceleration of a Loaded Wing in Response to a Linear Form of Vertical Gust. A.R.C. 10, 409, S. & C. 2021a, March 1947.Google Scholar
30. Sears, W. R. and Sparks, B. O. (1941). On the Reaction of an Elastic Wing to Vertical Gusts. Journal of the Aeronautical Sciences, Vol. 9, January 1941, pp. 64–67.Google Scholar
31. Küssner, H. G. (1940). Allgemeine Tragflächen-theorie. Luftfahrtforschung, Vol. 17, 1940, pp. 370–378.Google Scholar
32. Schwarz, L. (1940). Berechnung der Druckverteilung einer harmonisch sich verformenden Tragfläche in ebener Strömung. Luftfahrtforschung, Vol. 17, 1940, pp. 379–386.Google Scholar
33. Reissner, E. (1944). On the General Theory of Thin Airfoils for Non-uniform Motion. N.A.C.A. T.N. No. 946, 1944.Google Scholar
34. Reissner, E. (1947). Effect of Finite Span on the Airload Distributions for Oscillating Wings. I. Aerodynamic Theory of Oscillating Wings of Finite Span. N.A.C.A. T.N. No. 1194, 1947. 29. Google Scholar
35. Reissner, E. (1947). II. Methods of Calculation and Examples of Application. N.A.C.A. T.N. No. 1195, 1947.Google Scholar
36. Küssner, H. G. (1931). Beanspruchung von Flugzeugflügeln durch Böen. Z.F.M., Vol. 22, 1931, pp. 579–586, 605-615.Google Scholar
37. Dörr, J. (1949). Détermination des forces aérodynamiques instationnaire. O.N.E.R.A., Paris, 1949.Google Scholar
38. Greidanus, J. H. and van Heemert, A. (1949). Theory of the Oscillating Aerofoil in Two-dimensional Incompressible Flow. Nat. Luchtvaartlab., Amsterdam. Report F.41.Google Scholar
39. Strang, W. J. (1948). A Physical Theory of Supersonic Aerofoils in Unsteady Flow. Proc. Roy. Soc. A, Vol. 195, 1948, pp. 245–264.Google Scholar
40. Schwarz, L., (1943). Ebene instationäre Theorie der Tragfläche bei Uberschallgeschwindig- keit. Lufo, 1943, I.A. 010 (also M.A.P. Volkenröde V.G.59-188T.).Google Scholar
41. Radok, J. R. M. (1949). Gustloads on Two-dimensional Aerofoils in Supersonic Flow. Australian Aero. Res. Labs. Report A.66 and S.M.142, December 1949.Google Scholar
42. Strang, W. J. (1949). Transient Lift of Purely Supersonic Wings. Australian Aero. Res. Labs. Report A.61.Google Scholar
43. Sears, W. R. (1940). Operational Methods in the Theory of Airfoils in Non-uniform Motion. Journal of Franklin Institute, July 1940, pp. 95–111.Google Scholar