Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T06:24:01.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Some accurate solutions of the lifting surface integral equation

Published online by Cambridge University Press:  17 February 2009

E. O. Tuck
E. O. Tuck
Affiliation:
Applied Mathematics Department, The University of Adelaide, S.A. 5005, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note describes a simple numerical method for solution of the lifting surface integral equation of aerodynamics, and provides benchmark computations of up to 7 figure accuracy for flat rectangular wings of arbitrary aspect ratio. The nature of the large aspect ratio limit is also investigated numerically and asymptotically. This enables determination of the limiting behaviour near the wing tips, which is compared to the predictions of lifting line theory. Generalisations to non-rectangular wings are discussed.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 2 , October 1993 , pp. 127 - 144
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Ashley, H. and Landahl, L., Aerodynamics of wings and bodies (Addison—Wesley, New York, 1965).Google Scholar
[2]Dyke, M. Van, Perturbation methods in fluid mechanics (Academic Press, New York, 1964, Annotated edition, Parabolic Press, Stanford, 1975).Google Scholar
[3]Frink, N. T., “Lifting-surface theory for skewed and swept subsonic wings”, J. Aircraft 19 (1982) 519–524.CrossRefGoogle Scholar
[4]Guermond, Jean-Luc, “A generalized lifting-line theory for curved and swept wings”, J. Fluid Mech. 211 (1990) 291–317.CrossRefGoogle Scholar
[5]Hauptmann, A. and Miloh, T., “On the exact solution of the linearized lifting-surface problem of an elliptic wing”, Quart. J. Mech. Appl. Math. 39 (1986) 41–66.CrossRefGoogle Scholar
[6]Kerwin, J. E. and Lee, C.-S., “Prediction of steady and unsteady marine propellor performance by numerical lifting surface theory”, Soc. Nav. Arch. Mar. Engrs Trans. 86 (1978) 218–253.Google Scholar
[7]Koerniawan, B., “Numerical solution of Prandtl's lifting-line equation”, M. Sc. Thesis, University of Adelaide, 1992.Google Scholar
[8]Oertel, R. P., “The steady motion of a flat ship, including an investigation of local flow near the bow”, Ph. D. Thesis, University of Adelaide, 1975.Google Scholar
[9]Stewartson, K., “A note on lifting line theory”, Quart. J. Mech. Appl. Math. 13 (1960) 49–56.CrossRefGoogle Scholar
[10]Thwaites, B., Incompressible aerodynamics (Oxford Univ. Press, Oxford, 1960).CrossRefGoogle Scholar
[11]Tuck, E. O., “Application and numerical solution of Cauchy-singular integral equations”, in The application and numerical solution of integral equations (eds. Anderssen, R. S. et al. ), (Sijthoff and Noordhoff, The Netherlands, 1980).Google Scholar
[12]Tuck, E. O., “Planing surfaces”, in Numerical solution of integral equations (ed. Golberg, M.), (Plenum Press, New York, 1990).Google Scholar
[13]Varley, E. and Walker, J. D. A., “A method for solving singular integrodifferential equations”, Inst. Math. Appl. J. Applied Math. 43 (1989) 11–45.CrossRefGoogle Scholar
[14]Wang, H. T., “Comprehensive evaluation of six thin-wing lifting-surface computer programs”, David Taylor Naval Research Center Rep. 4333 (1974).Google Scholar
[15]Xü, Hongbo, “Potential flow solution for a yawed surface-piercing plate”, J. Fluid Mech. 226 (1991) 291–317.CrossRefGoogle Scholar