1965 Fluid Dynamics Transactions  
Except for particular examples which have fundamental interest rather than engineering utility, exact solutions to loading problems on three-dimensional lifting surfaces have proved unobtainable even by small-perturbatian methods. Beginning with the eminently successful liftingline idealization, there has resulted a proliferation of theories embodying various physical and consistent or inconsistent mathematical approximations. Nearly all of these are now rendered obsolete by the general
more » ... lity of digital computation machinery with extraordinary speed and capacity, because the best engineering approach is now unquestionably through numerical treatment of the exact linearized integral equation appropriate to the problem under consideration. A useful by-product of these developments is that the erstwhile restriction to a single, isolated wing whose mean surface lies close to one coordinate plane no longer need be accepted. Integral representations car, be devised for the coupled flow fields due to aggregates of lifting surfaces, combinations of wings and bodies, or nonplanar mean surfaces. A number of applications of this modified approach to the phenomenon known as "interference" are described, some including numerical results and comparisons with experiment. Both steady flight and simple harmonic oscillatory motions of small amplitude are included in the examples. Those flows which involve an incompressible or subsonic main stream are constructed by superposition of properly-oriented doublets of acceleration potential; the singular behavior of the integrals is handled in the same manner as for a planar surface. In supersonic cases the technique adopted consists of an extension of the concept of velocity potential aerodynamic influence coefficients. Specialization to sonic flight speed is discussed, but here the linearization is permissible only when the motion is unsteady. The paper concludes with a review of related subjects, such as the importance of coupling with flow produced by wing thickness, the influence of a ground-plane, and approximate means of accounting for second-order nonlinearity in supersonic flight. * Work of Stenton and collaborators, as yet unpublished.
doi:10.1016/b978-0-08-011860-4.50003-3 fatcat:togeqypkxvbbthhcv3ncarunju