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    Chiocchia, G. Tordella, D. and Prössdorf, S. 1997. The Lifting Line Equation for a Curved Wing in Oscillatory Motion. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 77, Issue. 4, p. 295.


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  • Journal of Fluid Mechanics, Volume 153
  • April 1985, pp. 59-81

Unsteady lifting-line theory as a singular perturbation problem

  • Ali R. Ahmadi (a1) (a2) and Sheila E. Widnall (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112085001148
  • Published online: 01 April 2006
Abstract

Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting-line theory of James (1975), and points out a limitation in that of Van Holten (1975, 1976, 1977).

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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