Lifting-line theory for a swept wing at transonic speeds

The boundary-value problems describing the first-order corrections \[ O\left ( {\frac {1}{{AR}},\frac {1}{{AR}}\ln AR} \right )\] 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.