Abstract
The purpose of the present paper is to show that lifting-line theory can be easily derived by applying the method of asymptotic expansions to the integral equation given by lifting-surface theory, in contrast to Van Dyke's paper [1] in which lifting-line theory is derived by applying the method of matched asymptotic expansions to a partial differential equation. Moreover, the present paper shows that there is an error in Van Dyke's paper about the third-order inner approximation, and the corrected formula about the circulation is obtained.
Zusammenfassung
In dieser Arbeit wird eine neue theoretische Untersuchung der Theorie der tragenden Linie beschrieben. Sie geht von der Tragflächentheorie aus mit Hilfe von asymptotischen Reihenentwicklungen. Es wird gezeigt, dass die Traglinientheorie in der Behandlung von Van Dyke [1] einen Fehler in der inneren Entwicklung dritter Ordnung enthält, und die richtige Form für den Auftrieb wird berechnet.
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References
M. Van Dyke, J. Appl. Math. Mech.28, 1, 90–102 (1964).
H. Ashley andM. J. Landahl,Aerodynamics of Wings and Bodies, Addison-Wesley Pub. Co. Inc., New York (1965).
M. Van Dyke,Perturbation Methods in Fluid Mechanics, The Parabolic Press, Stanford, California (1975).
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Kida, T., Miyai, Y. An alternative treatment of lifting-line theory as a perturbation problem. Journal of Applied Mathematics and Physics (ZAMP) 29, 591–607 (1978). https://doi.org/10.1007/BF01601487
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DOI: https://doi.org/10.1007/BF01601487