Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Lifting-line theory for a swept wing at transonic speeds

Author: L. Pamela Cook
Journal: Quart. Appl. Math. 37 (1979), 177-202
MSC: Primary 76H05
DOI: https://doi.org/10.1090/qam/542990
MathSciNet review: 542990
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Abstract: The boundary-value problems describing the first-order corrections

$\displaystyle O\left( {\frac{1}{{AR}},\frac{1}{{AR}}\ln AR} \right)$

to two-dimensional flow about a lifting swept wing at transonic speeds $ \left( {{M_\infty } < 1} \right)$ are derived. The corrections are found by the use of the method of matched asymptotic expansions on the transonic small disturbance equations. The wing is at a sweep angle of $ O\left( {{{\left( {1 - M_\infty ^2} \right)}^{1/2}}} \right)$ in the physical plane, hence of $ O\left( 1 \right)$ in the transonic small disturbance plane. As has been noted for subsonic flow, the finite sweep angle necessitates the introduction of terms $ O\left( {{{\left( {AR} \right)}^{ - 1}}\ln AR} \right)$. These terms arise naturally in the matching process. Of particular interest is the derivation of the near field of a skewed lifting-line which is found by Mellin transform techniques. Also of interest is the fact that the influence of the nonzero sweep angle can be completely separated from the unswept solution.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/542990
Article copyright: © Copyright 1979 American Mathematical Society

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