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Unsteady lifting-line theory as a singular perturbation problem

Published online by Cambridge University Press:  20 April 2006

Ali R. Ahmadi
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Present address: Bolt Beranek and Newman Inc., Cambridge, Massachusetts 02238.
Sheila E. Widnall
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139


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).

Research Article
© 1985 Cambridge University Press

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